| Título: | Excursions and Local Limit Theorems for Bessel-like Random Walks |
| Autores: | Alexander, Kenneth S.; University of Southern California |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
excursion, Lamperti problem, random walk, Bessel process 60J10; 60J80 |
| Descripción: | 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 at a given time (uniformly in a large range of heights.) In particular, for certain drifts inversely proportional to $x$ up to smaller-order correction terms, we show that the probability of a first return to $0$ at time $n$ decays as a certain inverse power of $n$, multiplied by a slowly varying factor that depends on the drift correction terms. |
| Idioma: | No aplica |
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