Year: 2011
Type: preprint
Abstract: Consider the random walk $S_n=ξ_1+...+ξ_n$ with independent and identically distributed increments and negative mean $\mathbf Eξ=-m<0$. 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 $\mathbf P(M_τ>x)$, where $M_τ=\max_{0\le i
Source: arXiv (Cornell University)
Authors: Denisov, Denis, Wachtel, Vitali
Institutions: Cardiff University, Ludwig-Maximilians-Universität München
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2949148798