Question: Exercise 12.97 Consider the symmetric random walk on the line Z. Show that any invariant distribution satisfies n = 1 2 (n1 + n+1),

Exercise 12.97 Consider the symmetric random walk on the line Z. Show that any invariant distribution

π satisfies πn = 1 2 (πn−1 + πn+1), and deduce that the walk is null recurrent.

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