Uniformization (probability theory): Difference between revisions

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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=0-12-374451-2 |page=98}}</ref>) is a method to compute transient solutions of finite state [[continuous-time Markov chain]]s, by approximating the process by a [[discrete time Markov chain]].<ref name="ibe" /> The original chain is scaled by the fastest transition rate ''γ'', so that transitions occur at the same rate in every state, 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 GrassmanWinfried Grassmann 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==