Question: 1. Let X(t) : t 0 be a continuous-time Markov chain with state space S. Show that for i, j S and t

1. Let

X(t) : t ≥ 0


be a continuous-time Markov chain with state space S. Show that for i, j ∈ S and t ≥ 0,

P(t)=ikPky (t) - Vipij(t). kpi

In other words, prove Kolmogorov’s backward equations.

P(t)=ikPky (t) - Vipij(t). kpi

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