Question
Transcribed Text
Problem 3. Consider the following Markov chain on the state space Q = {2k, k =
- 2, -1,-0,1,2, -
} . If your current position is x = 2k, then the next step you
jump to 2.c = 2k+1 or x/2 = 2k-1 with equal probabilities.
(a) Let D = {2-N,2-N+1 -
,
1,2,
,
2N }, for some N > 1. Suppose you absorb
the chain when it hits Dc. Show that f(x) = log(x) is a harmonic function at
any x in D.
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