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A Combinatorial Approach to the Two-Sided Exit Problem for Left-Continuous Random Walks

Published online by Cambridge University Press:  25 June 2001

PHILIPPE MARCHAL
PHILIPPE MARCHAL
Affiliation:
CNRS and DMA, Ecole Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France (e-mail: marchal@dmi.ens.fr)
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Abstract

We present a combinatorial lemma that provides a new approach to the two-sided exit problem and related questions for left-continuous random walks (i.e., random walks on the integers whose negative steps have size − 1). Some applications to random walks on the circle are also derived.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 3 , May 2001 , pp. 251 - 266
Copyright
2001 Cambridge University Press

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