The gambler's ruin problem in path representation form

Oscar Bolina

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The gambler's ruin problem in path representation form

Oscar Bolina

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Abstract

We consider the classical one-dimensional random walk of a particle on the right-half real line. We assume that the particle is initially at position x=k, k > 0, and moves to the right with probability p or to the left with probability 1-p. We consider that the particle is absorbed at the origin without fixing the number of steps needed to get there. We calculate the probability P(x=k) that the particles end up at the origin, given that it starts at x=k, by means of a geometric representation of this random walk in terms of paths on a two-dimensional lattice.

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Oscar Bolina. 2001-11-22. The gambler's ruin problem in path representation form. https://arxiv.org/abs/math/0111242

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