Reversed compound agent theorem

{{Short description|Aspect of probability theory}}

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In probability theory, the reversed compound agent theorem (RCAT) is a set of sufficient conditions for a stochastic process expressed in any formalism to have a product form stationary distribution{{Cite journal | last1 = Harrison | first1 = P. G. | author-link = Peter G. Harrison| title = Turning back time in Markovian process algebra | doi = 10.1016/S0304-3975(02)00375-4 | journal = Theoretical Computer Science | volume = 290 | issue = 3 | pages = 1947–2013 | year = 2003 | doi-access = free }} (assuming that the process is stationary{{Cite journal | last1 = Harrison | first1 = P. G. | author-link = Peter G. Harrison| title = Process Algebraic Non-product-forms | doi = 10.1016/j.entcs.2006.03.012 | journal = Electronic Notes in Theoretical Computer Science | volume = 151 | issue = 3 | pages = 61–76 | year = 2006 | doi-access = free }}). The theorem shows that product form solutions in Jackson's theorem, the BCMP theorem{{Cite journal | last1 = Harrison | first1 = P. G. | author-link = Peter G. Harrison| doi = 10.1016/j.laa.2004.02.020 | title = Reversed processes, product forms and a non-product form | journal = Linear Algebra and Its Applications | volume = 386 | pages = 359–381| year = 2004 | doi-access = }} and G-networks are based on the same fundamental mechanisms.{{Cite book | last1 = Hillston | first1 = J. | author-link1 = Jane Hillston| chapter = Process Algebras for Quantitative Analysis | doi = 10.1109/LICS.2005.35 | title = 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05) | pages = 239–248 | year = 2005 | isbn = 0-7695-2266-1 | s2cid = 1236394 | chapter-url = http://www.dcs.ed.ac.uk/pepa/quantitativeanalysis.pdf}}

The theorem identifies a reversed process using Kelly's lemma, from which the stationary distribution can be computed.