Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 411-422
doi:10.1155/S104895339400033X

A further study of an approximation for last-exit and first-passage probabilities of a random walk

D. J. Daley1 and L. D. Servi2

1Australian National University, School of Mathematical Sciences, Centre for Mathematics and its Applications, A.C.T., 0200, Australia
2GTE Laboratories Incorporated, 40 Sylvan Road, Waltham 02254, MA, USA

Received 1 April 1994; Revised 1 July 1994

Copyright © 1994 D. J. Daley and L. D. Servi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Identities between first-passage or last-exit probabilities and unrestricted transition probabilities that hold for left- or right-continuous lattice-valued random walks form the basis of an intuitively based approximation that is demonstrated by computation to hold for certain random walks without either the left- or right-continuity properties. The argument centers on the use of ladder variables; the identities are known to hold asymptotically from work of Iglehart leading to Brownian meanders.