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February 2018 On the exit time from an orthant for badly oriented random walks
Rodolphe Garbit
Braz. J. Probab. Stat. 32(1): 117-146 (February 2018). DOI: 10.1214/16-BJPS334

Abstract

It was recently proved that the exponential decreasing rate of the probability that a random walk stays in a $d$-dimensional orthant is given by the minimum on this orthant of the Laplace transform of the random walk increments, provided that this minimum exists. In other cases, the random walk is “badly oriented” and the exponential rate may depend on the starting point $x$. We show here that this rate is nevertheless asymptotically equal to the infimum of the Laplace transform, as some selected coordinates of $x$ tend to infinity.

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Rodolphe Garbit. "On the exit time from an orthant for badly oriented random walks." Braz. J. Probab. Stat. 32 (1) 117 - 146, February 2018. https://doi.org/10.1214/16-BJPS334

Information

Received: 1 September 2015; Accepted: 1 August 2016; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06973951
MathSciNet: MR3770866
Digital Object Identifier: 10.1214/16-BJPS334

Keywords: cones , Exit time , Laplace transform , Random walk

Rights: Copyright © 2018 Brazilian Statistical Association

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Vol.32 • No. 1 • February 2018
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