Random walks in cones
By Denis Denisov, Vitali Wachtel. 2011
208 citations recorded by the source corpus.
We study the asymptotic behavior 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 tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Brownian motion. For the proof of local limit theorems, we suggest a rather simple approach, which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks. We also discuss some possible applications of our results to ordered random walks and lattice path enumeration.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/033d4ddafd12db5e63c1356a77e6314de7b602ad
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In Artificial Intelligence
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Random walks in the quarter plane, discrete harmonic functions and conformal mappings (2013, background): “Random processes conditioned on staying in cones of Z arouse a great interest in the mathematical community, as they appear in several distinct domains: quantum random walks [3, 5], random matrices [11], non-colliding random walks [8, 9, 12], etc.”