An Algorithm to Compute the Equilibrium Distribution of a One-Dimensional Bounded Random Walk

1 June 1986

journal article
Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research

Vol. 34 (3) , 449-454
https://doi.org/10.1287/opre.34.3.449

Abstract

We present an algorithm that is suitable for finding the equilibrium distribution of a one-dimensional random walk in the presence of one or more boundaries. The method involves the evaluation of a “reduced” difference equation whose coefficients are found to have the very useful property of being insensitive to small changes in the parameters of the random walk and to rounding errors in the computation.

Keywords

EQUILIBRIUM DISTRIBUTION
RANDOM WALK
DIMENSIONAL RANDOM
USEFUL PROPERTY
SMALL CHANGES
ROUNDING ERRORS
METHOD INVOLVES
BOUNDED RANDOM

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