Electronic Communications in Probability

Electronic Communications in Probability > Vol. 9 (2004) > Paper 16

A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk

Antal A Jarai, Carleton University, Canada
Harry Kesten, Cornell University

Abstract
We consider a random walk $S_n = sum_{i=1}^n X_i$ with i.i.d. $X_i$. We assume that the $X_i$ take values in $Bbb Z^d$, have bounded support and zero mean. For $A subset Bbb Z^d, A ne emptyset$ we define $tau_A = inf{n ge 0: S_n in A}$. We prove that there exists a constant $C$, depending on the common distribution of the $X_i$ and $d$ only, such that $sup_{emptyset ne A subset Bbb Z^d} P{tau_A =n} le C/n, n ge 1$.

Full text: PDF

Pages: 152-161

Published on: November 17, 2004

Bibliography

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Electronic Communications in Probability. ISSN: 1083-589X