Ergodicity for multidimensional jump diffusions with position dependent jump rate

Eva Löcherbach; Victor Rabiet

doi:10.1214/16-AIHP750

Ergodicity for multidimensional jump diffusions with position dependent jump rate

Eva Löcherbach
, Victor Rabiet

CY Cergy Paris Université
Université Gustave Eiffel

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider a jump type diffusion X = (Xt )t with infinitesimal generator given by (equation presented) where μ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.

Original language	English
Pages (from-to)	1136-1163
Number of pages	28
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1214/16-AIHP750
Publication status	Published - 1 Aug 2017
Externally published	Yes

Keywords

Additive functionals
Continuous time Markov processes
Diffusions with jumps
Harris recurrence
Nummelin splitting

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10.1214/16-AIHP750

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abstract = "We consider a jump type diffusion X = (Xt )t with infinitesimal generator given by (equation presented) where μ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.",

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author = "Eva L{\"o}cherbach and Victor Rabiet",

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AU - Rabiet, Victor

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PY - 2017/8/1

Y1 - 2017/8/1

N2 - We consider a jump type diffusion X = (Xt )t with infinitesimal generator given by (equation presented) where μ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.

AB - We consider a jump type diffusion X = (Xt )t with infinitesimal generator given by (equation presented) where μ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.

KW - Additive functionals

KW - Continuous time Markov processes

KW - Diffusions with jumps

KW - Harris recurrence

KW - Nummelin splitting

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

Ergodicity for multidimensional jump diffusions with position dependent jump rate

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