| Título: | Stability Properties of Constrained Jump-Diffusion Processes |
| Autores: |
Atar, Rami; Technion - Israel Institute of Technology Budhiraja, Amarjit; University of North Carolina |
| Fecha: | 2002-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Jump diffusion processes. The Skorohod map. Stability cone. Harris recurrence. 60J60 60J75 (34D20, 60K25) |
| Descripción: | 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 ${\cal C}^o$. |
| Idioma: | Inglés |
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