The one-dimensional random walk with absorption is the following Markov model:

? There are 2N + 1 states, labelled ?N, . . . ? 1, 0, 1 . . . N.

? if k != ?N, N then there are two transitions from K, to K ?1

and K + 1, each with probability 1/2.

? The only transition from N and from ?N is to itself with

probability 1. The picture below illustrates the model with N = 3.

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