Revista Matemática Iberoamericana
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Published online: 2016-06-08
On the exit time from a cone for random walks with driftRodolphe Garbit and Kilian Raschel (1) Université François Rabelais, Tours, France
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.
Keywords: Random walk, cones, exit time, Laplace transform
Garbit Rodolphe, Raschel Kilian: On the exit time from a cone for random walks with drift. Rev. Mat. Iberoam. 32 (2016), 511-532. doi: 10.4171/RMI/893