6 Suppose Yt is a continuous time Markov chain with infinitesimal generator Let v be a column eigenvector of with eigenvalue Show that Xt etvYt is a martingale in the sense that E(Xt s Yr, r 0, t ) Xt Here vYt is coordinate Yt of v ...

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=+6. Suppose Yt is a continuous-time Markov chain with infinitesimal generator . Let v be a column

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=+6. Suppose Yt is a continuous-time Markov chain with infinitesimal generator Ω. Let v be a column eigenvector of Ω with eigenvalue λ. Show that Xt = e−λtvYt is a martingale in the sense that E(Xt+s | Yr, r ∈ [0, t]) = Xt.

Here vYt is coordinate Yt of v.

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Applied Probability

ISBN: 9781441971647

2nd Edition

Authors: Kenneth Lange

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Question Posted: Nov 01, 2024 04:00 AM

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=+6. Suppose Yt is a continuous-time Markov chain with infinitesimal generator . Let v be a column

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Applied Probability

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