Uniformization (probability theory): Difference between revisions

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with <math>\gamma</math> chosen such that <math>\gamma \geq \max_i |q_{ii}|</math>.
Randomizing the discrete-time Markov chain now results in the following formula for the solution of the <math>P(t)</math>, the transient solution of the continuous-time Markov chain
 
::<math>P(t) = \sum_{n=0}^{\infty} P^n e^{\gamma t} (\gamma t)^n/n!</math>