## Brazilian Journal of Probability and Statistics

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

Rodolphe Garbit

#### 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.

#### Article information

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

Dates
Accepted: August 2016
First available in Project Euclid: 3 March 2018

https://projecteuclid.org/euclid.bjps/1520046137

Digital Object Identifier
doi:10.1214/16-BJPS334

Mathematical Reviews number (MathSciNet)
MR3770866

Zentralblatt MATH identifier
06973951

#### Citation

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. https://projecteuclid.org/euclid.bjps/1520046137

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