Grinstead-Snell-Probability · Problem 11.2.31

Markov Chains

Mathematics · absorbing-markov-chains

Problem

In Example 11.11, define f(i)f(i) to be the proportion of G genes in state ii. Show that ff is a harmonic function (see Exercise 27). Why does this show that the probability of being absorbed in state (GG, GG) is equal to the proportion of G genes in the starting state? (See Exercise 17.)

Related theory

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