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• W2952010026 abstract "We consider reflecting random walks on the nonnegative integers with drift of order 1/x at height x. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of 0 and first return time to 0, and the probability of being at a given height k at time n (uniformly in a large range of k.) In particular, for drift of form -delta/2x + o(1/x) with delta > -1, we show that the probability of a first return to 0 at time n is asymptotically n^{-c}phi(n), where c = (3+delta)/2 and phi is a slowly varying function given explicitly in terms of the o(1/x) terms." @default.
• W2952010026 created "2019-06-27" @default.
• W2952010026 creator A5020849093 @default.
• W2952010026 date "2009-12-23" @default.
• W2952010026 modified "2023-09-27" @default.
• W2952010026 title "Excursions and local limit theorems for Bessel-like random walks" @default.
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