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Typical long time behaviour of ground state-transformed jump processes

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journal contribution
posted on 16.11.2018, 14:18 authored by Kamil Kaleta, Jozsef Lorinczi
We consider a class of Levy-type processes derived via a Doob-transform from Levy 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 Levy generators perturbed by the potential. We derive precise lower and upper envelopes for the almost sure long time behaviour of these ground state-transformed Levy processes, characterized through escape rates and integral tests. We also highlight the role of the parameters by specific examples.

Funding

The research of K. Kaleta was supported by the National Science Center, Poland, grant 2015/17/B/ST1/0123.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Contemporary Mathematics

Volume

22

Issue

02

Citation

KALETA, K. and LORINCZI, J., 2018. Typical long time behaviour of ground state-transformed jump processes. Communications in Contemporary Mathematics, Doi: 10.1142/S0219199719500020.

Publisher

© World Scientific Publishing

Version

AM (Accepted Manuscript)

Publisher statement

Electronic version of an article published as Communications in Contemporary Mathematics, 22(02): 1950002, 2020, https://doi.org/10.1142/S0219199719500020 © [copyright World Scientific Publishing Company] https://www.worldscientific.com/worldscinet/ccm

Acceptance date

13/11/2018

Publication date

2019-02-18

Copyright date

2020

ISSN

0219-1997

eISSN

1793-6683

Language

en

Article number

1950002