Random Walks in Cones

Details Random Walks in Cones Random Walks in Cones

2011-10-06

arxiv.org/abs/1110.1254v1

Mathematics

Probability

33 pages

Scientific paper

We study the asymptotic behaviour of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of all asymptotic relations we use the strong approximation of random walks by the Brownian motion.

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