Uniformization (probability theory): Difference between revisions

Revision as of 18:27, 15 December 2011

Revision as of 18:11, 1 February 2012

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In [[probability theory]], '''uniformization''' method, (also known as '''Jensen's method'''<ref name="stewart" /> or the '''randomization method'''<ref name="ibe">{{cite book |title=Markov processes for stochastic modeling |last=Ibe |first=Oliver C. |year=2009 |publisher=[[Academic Press]] |isbn=0123744512 |page=98}}</ref>) is a method to compute transient solutions of finite state [[continuous-time Markov chain]]s. The method involves the constructions of an analgousanalogous [[discrete time Markov chain]],<ref name="ibe" /> where transitions occur according to an exponential distribution with the same parameter in every state. This parameter, ''γ'', is the same in all states hence the name ''uniform''isation. The method is simple to program and efficiently calculates an approximation to the transient distribution at a single point in time (near zero).<ref name="stewart" /> The method was first introduced by Grassman in 1977.<ref>{{cite jstor|172104}}</ref><ref>{{cite doi|10.1016/0305-0548(77)90007-7}}</ref><ref>{{cite doi|10.1016/0377-2217(77)90049-2}}</ref>

==Method description==

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==External links==

*[http://www.sis.pitt.edu/~dtipper/2130/unifm.m Matlab implementation]