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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 [[continuous-time Markov
For a continuous time Markov chain with transition rate matrix ''Q'', the uniformized discrete time Markov chain has probability transition matrix ''P'' calculated by<ref name="stewart">{{cite book |title=Probability, Markov chains, queues, and simulation: the mathematical basis of performance modeling|last=Stewart |first=William J. |year=2009 |publisher=[[Princeton University Press]] |isbn=0691140626 |page=361}}</ref><ref name="cass">{{cite book |title=Introduction to discrete event systems|last=Cassandras |first=Christos G. |last2=Lafortune| first2=Stéphane|year=2008 |publisher=Springer |isbn=0387333320}}</ref><ref name="ross">{{cite book |title=Introduction to probability models|last=Ross |first=Sheldon M. |year=2007 |publisher=Academic Press |isbn=0125980620}}</ref>
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::<math>p_{ij} = \begin{cases} q_{ij}/\gamma &\text{ if } i \neq j \\ 1 - \sum_{j \neq i} q_{ij}/\gamma &\text{ if } i=j \end{cases}</math>
with <math>\gamma</math> chosen such that
::<math>\gamma \geq \max_i |\sum_{j} q_{ij}|.</math> Randomizing the discrete-time Markov chain now results in the following formula for the solution of <math>P(t)</math>, the transient solution of the continuous-time Markov chain
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