Consider a frog jumping from a lotus leaf to a lotus leaf on in a small forest pond. Suppose that there are N leaves so that the state space can be described as S = {1,2,...,N}. The frog starts on leaf 1 at time n = 0, and jumps around in the following fashion: at time 0 it chooses any leaf except for the one it is currently sitting on (with equal probability) and then jumps to it. At time n > 0, it chooses any leaf other than the one it is sitting on and the one it visited immediately before (with equal probability) and jumps to it. The position {Xn}n∈N0 of the frog is not a Markov chain.
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