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Typical long time behaviour of ground state-transformed jump processes
journal contributionposted on 2018-11-16, 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.
The research of K. Kaleta was supported by the National Science Center, Poland, grant 2015/17/B/ST1/0123.
- Mathematical Sciences
Published inCommunications in Contemporary Mathematics
CitationKALETA, 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
- AM (Accepted Manuscript)
Publisher statementElectronic 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