Bounds on Absorption Probabilities for the m -Dimensional Random Walk
Abstract 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 multivariate normal, independent, but not necessarily identical. 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 regularity conditions the upper bound is shown to be a geometrically decreasing sequence. An application to the nonstationary stochastic cash balance problem is suggested.