Bounds on Absorption Probabilities for the m-Dimensional Random Walk.

摘要

Simple procedures are given for computing an upper bound on the probability that an m-dimensional random walk has not been absorbed by step n. The increments of the walk are distributed independently,but not necessarily identically. The upper bound may be computed without knowledge of the means of the increment,the shapes of the nonabsorbing regions,or the starting point of the walk. The absorbing regions may also change with time. Under certain conditions the upper bound is shown to be a geometrically decreasing sequence. Computational examples are given. An application to convergence of the Eppen-Fama stochastic cash balance problem in horizon length is suggested.