Typical long time behaviour of ground state-transformed jump processes

Abstract

We consider a class of Lévy-type processes derived via a Doob-transform from Lévy processes conditioned by a control function called potential. These processes have position-dependent and generally unbounded components, with stationary distributions given by the ground states of the Lévy generators perturbed by the potential. We derive precise lower and upper envelopes for the almost sure long time behaviour of these ground state-transformed Lévy processes, characterized through escape rates and integral tests. We also highlight the role of the parameters by specific examples.

arXiv comment27 pages

References in corpus (3)

• Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Lévy processes
• Multifractal properties of sample paths of ground state-transformed jump processes
• Functional central limit theorems and $P(phi{)}_1$-processes for the classical and relativistic Nelson models

Cited by in corpus (1)

• Multifractal properties of sample paths of ground state-transformed jump processes