Year: 2012
Type: preprint
Abstract: This article deals with the asymptotic behaviour as $t\to +\infty$ of the survival function $P[T > t],$ where $T$ is the first passage time above a non negative level of a random process starting from zero. In many cases of physical significance, the behaviour is of the type $P[T > t]=t^{-θ+ o(1)}$ for a known or unknown positive parameter $θ$ which is called a persistence exponent. The problem is well understood for random walks or Lévy processes but becomes more difficult for integrals of such processes, which are more related to physics. We survey recent results and open problems in this field.
Source: arXiv (Cornell University)
Authors: Aurzada, Frank, Simon, Thomas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1562019533