Let N denote the number of times that an asymmetric random walk that takes a step to the right with probability p and a step to the left with probability q = 1 − p revisits its starting point. Show that the PMF of N is given by pN(n) = P[N = n] = β(1 − β)n n = 0, 1, 2,...

where β = |p − q|.

260 Markov Processes for Stochastic Modeling