| Título: | Martingale approach to subexponential asymptotics for random walks |
| Autores: |
Denisov, Denis E; Cardiff University Wachtel, Vitali; University of Munich |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
random walk; supremum; cycle maximum; heavy-tailed distribution; stopping time 60G70;60K30; 60K25 |
| Descripción: | Consider the random walk $S_n=\xi_1+\cdots+\xi_n$ with independent and identically distributed increments and negative mean $\mathbf E\xi=-m<0$. Let $M=\sup_{0\le i} S_i$ be the supremum of the random walk. In this note we present derivation of asymptotics for $\mathbf P(M>x), x\to\infty$ for long-tailed distributions. This derivation is based on the martingale arguments and does not require any prior knowledge of the theory of long-tailed distributions. In addition the same approach allows to obtain asymptotics for $\mathbf P(M_\tau>x)$, where $M_\tau=\max_{0\le i<\tau}S_i$ and $\tau=\min\{n\ge 1: S_n\le 0 \}$. |
| Idioma: | Inglés |
1 On the Non-Convexity of the Time Constant in First-Passage Percolation por Kesten, Harry; Cornell University | 6 Simulations and Conjectures for Disconnection Exponents por Puckette, Emily E.; Occidental College,Werner, Wendelin; Université Paris-Sud and IUF |
2 A Proof of a Conjecture of Bobkov and Houdré por Kwapien, S.; Warsaw University,Pycia, M.; Warsaw University,Schachermayer, W.; University of Vienna | 7 Excursions Into a New Duality Relation for Diffusion Processes por Jansons, Kalvis M.; University College London |
3 Moderate Deviations for Martingales with Bounded Jumps por Dembo, Amir; Stanford University | 8 Percolation Beyond $Z^d$, Many Questions And a Few Answers por Benjamini, Itai; Weizmann Institute of Science,Schramm, Oded; Microsoft Research |
4 Bounds for Disconnection Exponents por Werner, Wendelin; Université Paris-Sud and IUF | 9 Transportation Approach to Some Concentration Inequalities in Product Spaces por Dembo, Amir; Stanford University,Zeitouni, Ofer; Technion - Israel Institute of Technology |
5 The Dimension of the Frontier of Planar Brownian Motion por Lawler, Gregory F.; Duke University | 10 Surface Stretching for Ornstein Uhlenbeck Velocity Fields por Carmona, Rene; Princeton University,Grishin, Stanislav; Princeton University,Xu, Lin; Princeton University,Molchanov, Stanislav; University of North Carolina at Charlotte |