Boundary Behavior of Random Walks in Cones

K. Raschel, P. Tarrago

2020, v.26, Issue 4, 711-756

ABSTRACT

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.

Keywords: random walk, cone, exit time, harmonic function, Brownian motion

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Laboratory of large random systems, Dept. of Mechanics and Mathematics
Moscow State University, Vorobievy Gory, 119952 Moscow Russia
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The journal was founded in 1995 by prof. Malyshev V. A.
Published by Polymat Publishing Company, Moscow, Russia
ISSN 1024-2953
The journal is published quaterly

Markov Processes And Related Fields

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K. Raschel, P. Tarrago