:User:Helgus/ Eventology and its applications
The basic achievements of mathematical eventology in actual fileds of application are:
- eventological portfolio analysis (statement and the decision of inverse eventological Markowitz’s problems (Harry Markovitz{{ref|Markowitz}}, the Nobel Prize on economy, 1990);
- eventological models of supply and demand (eventological substantiation and expanded interpretation of classical market «Marchall’s cross»{{ref|Marshall}} - «supply and demand cross»);
- eventological interpretation of [http://cogprints.org/2925/01/Mentalism_&_Behaviorism.pdf Herrnstein’s experiment with pigeons (1961) in psychology]{{ref|Herrnstein}} («The mind appears there and then, where and when there is an ability to make a probabilistic choice» - Vladimir Lefebvre, University of California at Irvin{{ref|Lefebvre}}, 2003);
- eventological models of «Vickrey auctions»{{ref|Vickrey}} (William Vickrey, the Nobel Prize on economy, 1996);
- eventological basis and expansion of prospect theory (Daniel Kahneman{{ref|Kahneman}} and Amos Tversky{{ref|Tversky}}) (Daniel Kahneman, the Nobel Prize on economy, 2002);
- eventological generalization of methods of experimental economics{{ref|Smith}} (Vernon Smith, the Nobel Prize on economy, 2002); and also in
- [http://www.amazon.com/gp/sitbv3/reader/ref=sib_dp_pt/103-2974729-5527057?%5Fencoding=UTF8&asin=0471937576 statistical geometry] (Dietrich Stoyan): the [http://www.bs-books.ru/ws/14/1389.htm new notion of set-means for random sets (1975).]{{ref|StoyanStoyan}}
Following fields have been developed recently:
- eventological theory of dependencies{{ref|Frechet}} of random events including theory of eventological copula{{ref|Nelsen}};
- eventological system analysis,
- eventological decision theory and
- eventological theory of set-preferences (eventological explanation for a long time known Blyth’s paradox{{ref|Blyth}} in preference theory).
Applications of eventological theory
- Eventological theory of fuzzy events
- Eventological foundation of Kahneman and Tversky theory
- Eventological portfolio analysis
- Eventological system analysis
- Eventology of making decision
- Eventological theory of set-preferences
- Eventological foundation of economics
- Eventological scoring
- Eventological direct and inverse Markowitz's problems
- Eventological market "Marshall's Cross"
- Eventological explaination of K.Blayh's paradox in theory of preferences
References
- {{note|Blyth}} Blyth C.R. (1972) On Simpson's Paradox and the Sure --- Thing Principle. - Journal of the American Statistical Association, June, 67, P.367-381.
- {{note|DuboisPrade}}Dubois D., H.Prade (1988) Possibility theory. - New York: Plenum Press.
- Feynman R.P. (1982) Simulating physics with computers. - International Journal of Theoretical Physics, Vol. 21, nos. 6/7, 467-488.
- {{note|Frechet}}Fr'echet M. (1935) G'en'eralisations du th'eor'eme des probabilit'es totales - Fundamenta Mathematica. - 25.
- [http://plato.stanford.edu/archives/sum2003/entries/probability-interpret Hajek, Alan (2003) Interpretations of Probability. - The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N.Zalta (ed.)]
- {{note|Herrnstein}}Herrnstein R.J. (1961) Relative and Absolute strength of Response as a Function of Frequency of Reinforcement. - Journal of the Experimental Analysis of Behavior, 4, 267-272.
- {{note|Kahneman}}Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decisios under risk. - Econometrica, 47, 313-327.
- {{note|Lefebvre}}Lefebvre V.A. (2001) Algebra of conscience. - Kluwer Academic Publishers. Dordrecht, Boston, London.
- {{note|Markowitz}}[http://r-events.narod.ru/0-papers/Markowitz1952-p0060.pdf Markowitz Harry (1952) Portfolio Selection. - The Journal of Finance. Vol. VII, No. 1, March, 77-91.]
- {{note|Marshall}}Marshall Alfred [http://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/marshall/ A collection of Marshall's published works]
- {{note|Nelsen}}Nelsen R.B. (1999) An Introduction to Copulas. - Lecture Notes in Statistics, Springer-Verlag, New York, v.139.
- {{note|Russell1}}Russell Bertrand (1945) A History of Western Philosophy and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day, New York: Simon and Schuster.
- {{note|Russell2}}Russell Bertrand (1948) Human Knowledge: Its Scope and Limits, London: George Allen & Unwin.
- Schrodinger Erwin (1959) Mind and Matter. - Cambridge, at the University Press.
- {{note|Shafer}}Shafer G. (1976). A Mathematical Theory of Evidence. – Princeton University Press.
- {{note|Smith}}[http://nobelprize.org/nobel_prizes/economics/laureates/2002/smith-lecture.pdf Smith Vernon (2002) Nobel Lecture.]
- {{note|StoyanStoyan}}Stoyan D., and H. Stoyan (1994) Fractals, Random Shapes and Point Fields. - Chichester: John Wiley & Sons.
- {{note|Tversky}}Tversky A., Kahneman D. (1992) Advances in prospect theory: cumulative representation of uncertainty. - Journal of Risk and Uncertainty, 5, 297-323.
- {{note|Vickrey}}Vickrey William [http://www.u.arizona.edu/~dreiley/papers/VickreyHistory.pdf Paper on the history of Vickrey auctions in stamp collecting]
- {{note|Zadeh1}}Zadeh L.A. (1965) Fuzzy Sets. - Information and Control. - Vol.8. - P.338-353.
- {{note|Zadeh2}}Zadeh L.A. (1968) Probability Measures of Fuzzy Events. - Journal of Mathematical Analysis and Applications. - Vol.10. - P.421-427.
- {{note|Zadeh3}}Zadeh L.A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. – Fuzzy Sets and Systems. - Vol.1. - P.3-28.
- {{note|Zadeh4}}Zadeh L.A. (2005). Toward a Generalized Theory of Uncertainty (GTU) - An Outline. - Information sciences (to appear).
- {{note|Zadeh5}}Zadeh L.A. (2005). Toward a computational theory of precisiation of meaning based on fuzzy logic - the concept of cointensive precisiation. - Proceedings of IFSA-2005 World Congress.} - Beijing: Tsinghua University Press, Springer.