Brazilian Journal of Probability and Statistics

On the exit time from an orthant for badly oriented random walks

Rodolphe Garbit

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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.

Article information

Braz. J. Probab. Stat., Volume 32, Number 1 (2018), 117-146.

Received: September 2015
Accepted: August 2016
First available in Project Euclid: 3 March 2018

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Zentralblatt MATH identifier

Random walk cones exit time Laplace transform


Garbit, Rodolphe. On the exit time from an orthant for badly oriented random walks. Braz. J. Probab. Stat. 32 (2018), no. 1, 117--146. doi:10.1214/16-BJPS334.

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