Year: 2019
Type: preprint
Abstract: In this paper we first provide several conditional limit theorems for Lévy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of heavy-tailed Lévy processes. As the key point, we observe that the asymptotics mainly depends on the sample paths with early arrival large jump. Both the polynomial decay rate and the exact expression of the limit coefficients are given. As an application, we give an exact description for the extinction speed of continuous-state branching processes in heavy-tailed Lévy random environment with stable branching mechanism.
Source: arXiv (Cornell University)
Author: Xu, Wei
Institution: Humboldt-Universität zu Berlin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2995030690