hw 7 - 4. Let (Xn , n ≥ 0) be a finite-state irreducible...

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Unformatted text preview: 4. Let (Xn , n ≥ 0) be a finite-state irreducible Markov chain with transition matrix P. Let f be a non-constant real-valued function and 0 < λ < 1 be such that j pij f (j ) = λf (i) ∀i. (i) Show that λ−n f (Xn ) is a martingale. (ii) Let τb be the first hitting time on a state b. Show that sup{θ : E (θτb |X0 = i) < ∞ ∀i} ≤ 1/λ. 7 ...
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This note was uploaded on 11/18/2009 for the course MATH 241 taught by Professor Reed during the Spring '09 term at Duke.

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