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Journal Articles Revista Matemática Iberoamericana Year : 2016

On the exit time from a cone for random walks with drift

Abstract

We compute the exponential decay of the probability that a given multi-dimensional random walk stays in a convex cone up to time $n$, as $n$ goes to infinity. We show that the latter equals the minimum, on the dual cone, of the Laplace transform of the random walk increments. As an example, our results find applications in the counting of walks in orthants, a classical domain in enumerative combinatorics.
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Dates and versions

hal-00838721 , version 1 (26-06-2013)
hal-00838721 , version 2 (28-06-2013)
hal-00838721 , version 3 (23-11-2013)
hal-00838721 , version 4 (27-05-2014)
hal-00838721 , version 5 (21-03-2015)

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Rodolphe Garbit, Kilian Raschel. On the exit time from a cone for random walks with drift. Revista Matemática Iberoamericana, 2016, 32 (2), pp.511-532. ⟨10.4171/rmi/893⟩. ⟨hal-00838721v5⟩
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