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2002 Stability Properties of Constrained Jump-Diffusion Processes
Rami Atar, Amarjit Budhiraja
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Electron. J. Probab. 7: 1-31 (2002). DOI: 10.1214/EJP.v7-121

Abstract

We consider a class of jump-diffusion processes, constrained to a polyhedral cone $G\subset\mathbb{R}^n$, where the constraint vector field is constant on each face of the boundary. The constraining mechanism corrects for ``attempts'' of the process to jump outside the domain. Under Lipschitz continuity of the Skorohod map $\Gamma$, it is known that there is a cone ${\cal C}$ such that the image $\Gamma\phi$ of a deterministic linear trajectory $\phi$ remains bounded if and only if $\dot\phi\in{\cal C}$. Denoting the generator of a corresponding unconstrained jump-diffusion by $\cal L$, we show that a key condition for the process to admit an invariant probability measure is that for $x\in G$, ${\cal L}\,{\rm id}(x)$ belongs to a compact subset of ${\cal C}^o$.

Citation

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Rami Atar. Amarjit Budhiraja. "Stability Properties of Constrained Jump-Diffusion Processes." Electron. J. Probab. 7 1 - 31, 2002. https://doi.org/10.1214/EJP.v7-121

Information

Accepted: 20 March 2002; Published: 2002
First available in Project Euclid: 16 May 2016

zbMATH: 1011.60061
MathSciNet: MR1943895
Digital Object Identifier: 10.1214/EJP.v7-121

Subjects:
Primary: 60J60 , 60J75
Secondary: 34D20 , 60K25

Keywords: Harris recurrence , Jump diffusion processes , Stability cone , The Skorohod map

Vol.7 • 2002
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