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Stability Properties of Constrained Jump-Diffusion Processes


 
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1. Title Title of document Stability Properties of Constrained Jump-Diffusion Processes
 
2. Creator Author's name, affiliation, country Rami Atar; Technion - Israel Institute of Technology
 
2. Creator Author's name, affiliation, country Amarjit Budhiraja; University of North Carolina
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Jump diffusion processes. The Skorohod map. Stability cone. Harris recurrence.
 
3. Subject Subject classification 60J60 60J75 (34D20, 60K25)
 
4. Description 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 ${\cal C}^o$.
 
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7. Date (YYYY-MM-DD) 2002-03-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/121
 
10. Identifier Digital Object Identifier 10.1214/EJP.v7-121
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 7
 
12. Language English=en en
 
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