WP:WikiProject Mathematics/PlanetMath Exchange/60-XX Probability theory and stochastic processes

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1051 Bayes' theorem], id=1051 -- WP: Bayes' theorem -- Status: A

::Ben Cairns 12:47, 1 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=517 Bernoulli random variable], id=517 -- WP: Bernoulli distribution -- Status: A

::AdamSmithee 15:43, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=530 beta random variable], id=530 -- WP: beta distribution -- Status: A

::AdamSmithee 15:43, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=551 chi-squared random variable], id=551 -- WP: chi-squared distribution -- Status: A

::AdamSmithee 15:43, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=496 continuous density function], id=496 -- WP: probability density function -- Status: A

::... but could use some clean-up. Ben Cairns 05:57, 2 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=505 expected value], id=505 -- WP: expected value -- Status: A

::Some minor deficiencies in the WP article were rectified, and the article refactored. Added reference to PM article. Ben Cairns 03:44, 2 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=529 Gamma random variable], id=529 -- WP: Gamma distribution -- Status: A

::AdamSmithee 17:35, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=520 geometric random variable], id=520 -- WP: geometric distribution -- Status: M

::Moment generating function.Also the WP article could use a Probability distribution infobox AdamSmithee 17:35, 4 January 2006 (UTC)

::Done AdamSmithee 08:37, 19 April 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5977 independent identically distributed], id=5977 -- WP: independent identically-distributed random variables -- Status: A

::Expanded on the WP article, removing an old stub notice in the process. PM article has a nice stochastic process example (interarrival times of a Poisson process), but it didn't seem necessary to add it in. Ben Cairns 05:55, 2 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=515 moment], id=515 -- WP: moment (mathematics), moment about the mean, skewness, kurtosis, leptokurtic, platykurtic -- Status: A

::WP articles contain all the same information and more, but could use some work. Ben Cairns 00:48, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3058 proof of Bayes' Theorem], id=3058 -- WP: Bayes' Theorem#Statement of Bayes' theorem -- Status: A

::PM article more directly general, but the WP article is easier to understand and is extended to the general case. Ben Cairns 12:45, 1 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=485 random variable], id=485 -- WP: random variable -- Status: M

::Merged in a little definitional stuff. The WP article still needs a bit of work, including possible merging with WP articles on continuous random variables and discrete random variables. Ben Cairns 04:04, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=525 uniform (continuous) random variable], id=525 -- WP: Uniform distribution (continuous) -- Status: A

::AdamSmithee 17:35, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=521 uniform (discrete) random variable], id=521 -- WP: uniform distribution -- Status: A

::AdamSmithee 17:35, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=510 variance], id=510 -- WP: variance -- Status: A

::... but only by a sentence or two. Ben Cairns 02:35, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6840 bibliography for probability], id=6840 -- WP guess: bibliography for probability -- Status: N

::List of textbooks AdamSmithee 14:07, 6 March 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9676 analytic solution to Ornstein-Uhlenbeck SDE], id=9676^new! -- WP guess: analytic solution to Ornstein-Uhlenbeck SDE -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8239 Buffon's needle], id=8239^new! -- WP guess: Buffon's needle -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7679 conditional expectation], id=7679^new! -- WP guess: conditional expectation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9165 conditional expectation under change of measure], id=9165^new! -- WP guess: conditional expectation under change of measure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9690 Monte Carlo simulation], id=9690^new! -- WP guess: Monte Carlo simulation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9675 Ornstein-Uhlenbeck process], id=9675^new! -- WP guess: Ornstein-Uhlenbeck process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8378 properties of expected value], id=8378^new! -- WP guess: properties of expected value -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4299 example of pairwise independent events that are not totally independent], id=4299 -- WP: pairwise independence -- Status: A

::Ben Cairns 05:40, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1053 independent], id=1053 -- WP: statistical independence -- Status: A

::Made a couple of minor corrections and a small addition. Ben Cairns 05:40, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3704 random event], id=3704 -- WP: event (probability theory) -- Status: A

::Ben Cairns 05:42, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8569 conditional independence], id=8569^new! -- WP guess: conditional independence -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8527 independent sigma algebras], id=8527^new! -- WP guess: independent sigma algebras -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2002 almost everywhere], id=2002 -- WP: almost everywhere, almost surely -- Status: A

::Tricky one. PM article covers both almost surely and almost everywhere, but seems more about the former. Special case of PM's example appears in WP's almost everywhere (along with other examples given in some complicated inline maths). PS: I've fixed the inline unpleasantness. Ben Cairns 13:09, 1 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=531 Cauchy random variable], id=531 -- WP: Cauchy distribution -- Status: A

::AdamSmithee 17:38, 4 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=576 joint continuous density function], id=576 -- WP: joint distribution -- Status: A

::WP article includes joint probability mass functions. Ben Cairns 01:46, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=571 joint cumulative distribution function], id=571 -- WP: joint distribution -- Status: NM

::Or just the information about distribution functions added without copying (it isn't much, really). Ben Cairns 01:46, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5846 neutrosophic probability], id=5846 -- WP: (none) -- Status: N

::Reliability of PM article has been questioned internally, it seems; related articles on neutrosophic sets and logic appear to have had WP versions deleted (they appear on google, but don't exist). So, this article does not seem appropriate for WP. Ben Cairns 05:59, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7220 neutrosophic probability], id=7220 -- WP: neutrosophic probability -- Status: N

::See above AdamSmithee 14:08, 6 March 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7768 \sigma-algebra generated by a random variable], id=7768^new! -- WP guess: \sigma-algebra generated by a random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8345 almost surely absolutely bounded random variable], id=8345^new! -- WP guess: almost surely absolutely bounded random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8356 convergence in probability is preserved under continuous transformations], id=8356^new! -- WP guess: convergence in probability is preserved under continuous transformations -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8568 probability conditioning on a sigma algebra], id=8568^new! -- WP guess: probability conditioning on a sigma algebra -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8346 relation between almost surely absolutely bounded random variables and their absolute moments], id=8346^new! -- WP guess: relation between almost surely absolutely bounded random variables and their absolute moments -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6049 Bonferroni inequalities], id=6049 -- WP: Boole's inequality -- Status: M

::Merged as a generalisation of Boole's inequality. Added redirect from Bonferroni inequalities. Ben Cairns 00:23, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3688 Borel-Cantelli lemma], id=3688 -- WP: Borel-Cantelli lemma -- Status: A

::But see the entries proof of Borelli-Cantelli 1 and 2 below. Ben Cairns 02:41, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3115 Chebyshev's inequality], id=3115 -- WP: Chebyshev's inequality -- Status: A

::Ben Cairns 03:03, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=504 cumulative distribution function], id=504 -- WP: cumulative distribution function -- Status: A

::... but could use some cleanup. Ben Cairns 03:12, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3448 distribution ensemble], id=3448 -- WP guess: distribution ensemble -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2817 Markov's inequality], id=2817 -- WP: Markov's inequality -- Status: A

::Ben Cairns 03:19, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5900 median of a distribution], id=5900 -- WP: median -- Status: M

::Added in examples of medians of several common distributions. Ben Cairns 04:01, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5889 mode], id=5889 -- WP guess: mode -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5992 proof of Borel-Cantelli 1], id=5992 -- WP: Borel-Cantelli lemma -- Status: NM

::Simple cut-and-paste should suffice. Ben Cairns 00:57, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6028 proof of Borel-Cantelli 2], id=6028 -- WP: Borel-Cantelli lemma -- Status: NM

::Simple cut-and-paste should suffice. Ben Cairns 00:57, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3116 proof of Chebyshev's inequality], id=3116 -- WP: Chebyshev's inequality#Proof -- Status: A

::Ben Cairns 03:03, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3111 proof of Markov's inequality], id=3111 -- WP: Markov's inequality#Proof -- Status: A

::Ben Cairns 03:19, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3446 pseudorandom], id=3446 -- WP: pseudorandom -- Status:

::The PM article's definition is particularly restrictive and (possibly) obscure. The WP article seems adequate but I will defer to a better-informed reader. If you are familiar with the mathematics of this topic please check the articles and update this entry appropriately. Ben Cairns 04:43, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3447 support], id=3447 -- WP: support -- Status: A

::WP article covers support more generally for functions and distributions. Noted that probability measures are measures. Ben Cairns 04:29, 4 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7195 corollary of Borel-Cantelli lemma], id=7195 -- WP guess: corollary of Borel-Cantelli lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8390 adapted process], id=8390^new! -- WP guess: adapted process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7705 Boole inequality], id=7705^new! -- WP guess: Boole inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7748 proof of Boole inequality], id=7748^new! -- WP guess: proof of Boole inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7916 criterion for almost-sure convergence], id=7916^new! -- WP guess: criterion for almost-sure convergence -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8574 regular conditional probability], id=8574^new! -- WP guess: regular conditional probability -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8581 symmetric random variable], id=8581^new! -- WP guess: symmetric random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6725 convergence in probability], id=6725 -- WP guess: convergence in probability -- Status: A

::PM article explicitly uses a general metric for the difference between X_n and X but I don't think this is necessary here. Ben Cairns 08:28, 12 April 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1914 multidimensional Gaussian integral], id=1914 -- WP: standardizing the multivariate normal distribution -- Status: NC

::A new article seems more appropriate than adding it to multivariate normal distribution. Ben Cairns 11:04, 6 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3454 binomial distribution], id=3454 -- WP: binomial distribution -- Status: NM

::The WP article lacks the generating function of a binomial and the derivation of the mean and variance. Also needs refactoring and general clean-up! Ben Cairns 11:15, 6 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3708 convergence in distribution], id=3708 -- WP: convergence of random variables -- Status: A

::Article covers all major modes of convergence of random variables. Made a couple of edits, but it was essentially all there. Ben Cairns 11:47, 6 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3711 Cramér-Wold theorem], id=3711 -- WP: Cramér-Wold theorem -- Status: C

::Ben Cairns 11:53, 6 Feb 2005 (UTC)

::User:Robbjedi

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3450 density function], id=3450 -- WP: probability mass function, probability density function -- Status: A

::The PM article starts with probability 'density' (should be 'mass') functions for discrete distributions, then extends to probability density functions for continuous distributions. It seems (from a quick scan) to contain an error in constructing the latter. Ben Cairns 03:36, 7 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3451 distribution function], id=3451 -- WP: cumulative distribution function -- Status: A

::Ben Cairns 21:55, 7 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3456 geometric distribution], id=3456 -- WP: geometric distribution -- Status: A

::A little extra derivation in PM article, so I added the p.g.f. and a link. Ben Cairns 04:30, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3431 Heaps' law], id=3431 -- WP: Heaps' law -- Status: A

::Long ago copied from PM; I added the copyright license notice. Ben Cairns 04:06, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3710 Helly-Bray theorem], id=3710 -- WP: Helly-Bray theorem -- Status: C

::Plus some additional material on a more general version of the theorem. Ben Cairns 23:11, 17 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=573 joint discrete density function], id=573 -- WP guess: joint discrete density function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=591 marginal distribution], id=591 -- WP guess: marginal distribution -- Status: A

::Ben Cairns 01:18, 15 Mar 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=512 moment generating function], id=512 -- WP: moment-generating function -- Status: A

::...following a couple of minor edits. Ben Cairns 01:32, 15 Mar 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6113 multinomial distribution], id=6113 -- WP guess: multinomial distribution -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6628 non-central chi-squared random variable], id=6628 -- WP guess: non-central chi-squared random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=527 normal random variable], id=527 -- WP: normal random variable -- Status: A

::AdamSmithee 14:36, 6 March 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1945 relative entropy], id=1945 -- WP guess: relative entropy -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3712 Scheffé's theorem], id=3712 -- WP guess: Scheffé's theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=511 standard deviation], id=511 -- WP: standard deviation -- Status: A

::AdamSmithee 14:36, 6 March 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5960 Weibull random variable], id=5960 -- WP: Weibull random variable -- Status: A

::AdamSmithee 14:36, 6 March 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3422 Zipf's law], id=3422 -- WP guess: Zipf's law -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7204 joint normal distribution], id=7204 -- WP guess: joint normal distribution -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8384 cumulant generating function], id=8384^new! -- WP guess: cumulant generating function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9497 degrees of freedom], id=9497^new! -- WP guess: degrees of freedom -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7935 Gumbel random variable], id=7935^new! -- WP guess: Gumbel random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9628 moment generating function of the sum of independent random variables], id=9628^new! -- WP guess: moment generating function of the sum of independent random variables -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8753 multivariate distribution function], id=8753^new! -- WP guess: multivariate distribution function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9833 table of probabilities of standard normal distribution], id=9833^new! -- WP guess: table of probabilities of standard normal distribution -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8582 type of a distribution function], id=8582^new! -- WP guess: type of a distribution function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8585 infinitely divisible random variable], id=8585^new! -- WP guess: infinitely divisible random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8584 stable random variable], id=8584^new! -- WP guess: stable random variable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3714 characteristic function], id=3714 -- WP: characteristic function -- Status: NM

::A bunch of properties of characteristic functions in the PM article do not appear in the WP article. Ben Cairns 12:00, 6 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3715 Paul Lévy continuity theorem], id=3715 -- WP: Lévy continuity theorem -- Status: NC

::We've needed this article for a while to complete the proof of the law of large numbers and the basic central limit theorem. Ben Cairns 12:00, 6 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3687 Kolmogorov's inequality], id=3687 -- WP: Kolmogorov's inequality -- Status: C

::Doesn't seem to appear elsewhere on WP. Ben Cairns 01:54, 16 Feb 2005 (UTC).

::Done User:Robbjedi

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6086 proof of Kolmogorov's inequality], id=6086 -- WP: Kolmogorov's inequality -- Status: NM

::...with the above article. Ben Cairns 01:54, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8267 a simple method for comparing real functions], id=8267^new! -- WP guess: a simple method for comparing real functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8333 absolute moments bounding (necessary and sufficient condition)], id=8333^new! -- WP guess: absolute moments bounding (necessary and sufficient condition) -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8302 Bennett inequality], id=8302^new! -- WP guess: Bennett inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8233 Bernstein inequalities], id=8233^new! -- WP guess: Bernstein inequalities -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8230 Chernoff-Cramer bound], id=8230^new! -- WP guess: Chernoff-Cramer bound -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8312 Prohorov inequality], id=8312^new! -- WP guess: Prohorov inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8303 proof of Bennett inequality], id=8303^new! -- WP guess: proof of Bennett inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8240 proof of Bernstein inequalities], id=8240^new! -- WP guess: proof of Bernstein inequalities -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8231 proof of Chernoff-Cramer bound], id=8231^new! -- WP guess: proof of Chernoff-Cramer bound -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8313 proof of Prohorov inequality], id=8313^new! -- WP guess: proof of Prohorov inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=486 discrete density function], id=486 -- WP: probability mass function -- Status: A

::Ben Cairns 11:48, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6252 law of rare events], id=6252 -- WP: Poisson distribution -- Status: A

::Could use some refactoring to synthesise the section on the law of small numbers with the law of rare events. Also added link to PM article. Ben Cairns 12:13, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2884 probability distribution function], id=2884 -- WP: probability distribution -- Status: NM

::PM article defines probability distribution functions as objects generalising both probability mass functions and probability density functions. Contrast common usage of distribution function as the cumulative distribution function, and probability distribution as something somewhat less general than a probability measure. Seems best merged with probability distribution, but we should stick with WP's established terminology (which I happen to be familiar with myself). Nonetheless, content from this article should make an excellent contribution. Ben Cairns 12:24, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3713 Lindeberg's central limit theorem], id=3713 -- WP: central limit theorem, Lyapunov's central limit theorem -- Status: NM

::There is some good content here, including a more general Lyapunov condition, that could be merged. The historical note is also interesting. Ben Cairns 12:37, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9679 tight and relatively compact measures], id=9679^new! -- WP guess: tight and relatively compact measures -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3686 Kolmogorov's strong law of large numbers], id=3686 -- WP: law of large numbers -- Status: NM

::The non-i.i.d. case is not covered by the WP article. Ben Cairns 12:29, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3685 strong law of large numbers], id=3685 -- WP: law of large numbers -- Status: NM

::As part of the merge for Kolmogorov's strong law of large numbers, above. Ben Cairns 12:29, 20 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6244 stochastic process], id=6244 -- WP: stochastic process -- Status: A

::...but could use some work to make the notation clearer. Ben Cairns 03:33, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7176 sample function], id=7176 -- WP guess: sample function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8245 modification of a stochastic process], id=8245^new! -- WP guess: modification of a stochastic process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6261 memoryless random variable], id=6261 -- WP: memorylessness -- Status: A

::Ben Cairns 04:13, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7183 distributions of a stochastic process], id=7183 -- WP guess: distributions of a stochastic process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7250 independent stochastic processes], id=7250 -- WP guess: independent stochastic processes -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6973 local martingale], id=6973 -- WP guess: local martingale -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7678 Kolmogorov's continuity theorem], id=7678^new! -- WP guess: Kolmogorov's continuity theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9694 Kolmogorov's martingale inequality], id=9694^new! -- WP guess: Kolmogorov's martingale inequality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8583 exchangeable random variables], id=8583^new! -- WP guess: exchangeable random variables -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6919 autocovariance function], id=6919 -- WP: autocovariance function -- Status: A

::added redirect AdamSmithee 09:44, 28 September 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7160 discrete white noise], id=7160 -- WP: white noise -- Status: A

::AdamSmithee 09:44, 28 September 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7168 mean square convergence of the sample mean of a stationary process], id=7168 -- WP guess: mean square convergence of the sample mean of a stationary process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7198 proof of mean square convergence of the sample mean of a stationary process], id=7198 -- WP guess: proof of mean square convergence of the sample mean of a stationary process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7207 stationary process], id=7207 -- WP guess: stationary process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7209 Gaussian process], id=7209 -- WP guess: Gaussian process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7940 Wiener measure], id=7940^new! -- WP guess: Wiener measure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6294 stopping time], id=6294 -- WP: Martingale -- Status: A

::WP's article is less formal (it avoids talking about filtrations), but seems adequate in the context. The concept of a filtration could be added to the article, but this might as well be done organically. Ben Cairns 03:29, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6267 Wald's equation], id=6267 -- WP: Wald's equation -- Status: C

::Ben Cairns 04:00, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8949 Doob's Optional Sampling Theorem], id=8949^new! -- WP guess: Doob's Optional Sampling Theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8948 gale], id=8948^new! -- WP guess: gale -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4157 martingale], id=4157^new! -- WP guess: martingale -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6694 random walk], id=6694 -- WP guess: random walk -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6730 counting process], id=6730 -- WP guess: counting process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6731 independent increment], id=6731 -- WP guess: independent increment -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6733 Poisson process], id=6733 -- WP guess: Poisson process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6732 stationary increment], id=6732 -- WP guess: stationary increment -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9610 Itô's formula], id=9610^new! -- WP guess: Itô's formula -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8706 analytic solution of Black-Scholes PDE], id=8706^new! -- WP guess: analytic solution of Black-Scholes PDE -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8675 Black-Scholes formula], id=8675^new! -- WP guess: Black-Scholes formula -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8697 Black-Scholes PDE], id=8697^new! -- WP guess: Black-Scholes PDE -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9699 derivation of Black-Scholes formula in martingale form], id=9699^new! -- WP guess: derivation of Black-Scholes formula in martingale form -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8323 Itô integral], id=8323^new! -- WP guess: Itô integral -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9158 no-arbitrage in the Black-Scholes pricing model], id=9158^new! -- WP guess: no-arbitrage in the Black-Scholes pricing model -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7941 Cameron-Martin space], id=7941^new! -- WP guess: Cameron-Martin space -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5765 class structure], id=5765 -- WP: Markov chain -- Status: A

::Added a ref. to the PM article. Ben Cairns 03:46, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5764 hitting time], id=5764 -- WP: Stochastic process -- Status: NM

::PM article is specific to Markov chains, but hitting times are a common quantity of interest in many stochastic processes. Ben Cairns 03:46, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2886 Markov chain], id=2886 -- WP: Markov chain -- Status: A

::Ben Cairns 03:24, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5807 mean hitting time], id=5807 -- WP: Markov chain -- Status: NM

::This is specific to Markov chains, and is such a common problem in applications that it should be merged into that article. Ben Cairns 03:46, 16 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8556 periodicity of a Markov chain], id=8556^new! -- WP guess: periodicity of a Markov chain -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8561 recurrence in a Markov chain], id=8561^new! -- WP guess: recurrence in a Markov chain -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8307 Feller process], id=8307^new! -- WP guess: Feller process -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8306 probability transition function], id=8306^new! -- WP guess: probability transition function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6974 Brownian motion], id=6974 -- WP guess: Brownian motion -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6975 Levy martingale characterization], id=6975 -- WP guess: Levy martingale characterization -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6976 wavelet representation of Brownian motion], id=6976 -- WP guess: wavelet representation of Brownian motion -- Status: