Escape time for a random walk from an orthant

L.A. Klein Haneveld and A.O. Pittenger

Stochastic Processes and their Applications, 1990, vol. 35, issue 1, 1-9

Abstract: Let {([xi]k, [eta]k), k>[greater-or-equal, slanted]} be a sequence of independent random vectors with values in {-1, 0, ...} x{-1, 0, ...}. Assume the component variables have zero means, bounded second moments, and that [alpha] = E[[xi]k[eta]k] is the same for all k. Let Zn denote (i0,j0)+[Sigma]n1 ([xi]k, where i0, j0 are positive integers, and let [tau] denote the first time Zn hits a coordinate axis. We show E([tau]) is finite if and only if [alpha]

Keywords: random; walk; martingales; stopping; times (search for similar items in EconPapers)
Date: 1990
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