| Título: | The Beurling Estimate for a Class of Random Walks |
| Autores: |
Lawler, Gregory F; Cornell University Limic, Vlada; University of British Columbia |
| Fecha: | 2004-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Beurling projection; random walk; Green's function; escape probabilities 60G50; 60F99 |
| Descripción: | An estimate of Beurling states that if $K$ is a curve from $0$ to the unit circle in the complex plane, then the probability that a Brownian motion starting at $-\varepsilon$ reaches the unit circle without hitting the curve is bounded above by $c \varepsilon^{1/2}$. This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was first proved by Kesten. In this note we extend this estimate to random walks with zero mean, finite $(3+\delta)$-moment. |
| Idioma: | No aplica |
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