posted on 2018-11-16, 14:18authored byKamil 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.