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Stability Properties of Constrained Jump-Diffusion Processes
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Rami Atar, Technion - Israel Institute of Technology
Amarjit Budhiraja, University of North Carolina
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Abstract
We consider a class of jump-diffusion processes,
constrained to a polyhedral cone G of Rn, 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 C such that
the image Gamma phi of a deterministic linear
trajectory phi remains bounded if and only if
dot{phi}in C.
Denoting the generator of a corresponding unconstrained jump-diffusion
by L, we show that a key condition for the process
to admit an invariant probability measure is that for all x in
G, L id (x) belongs to a compact subset of
Co.
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Full text: PDF
Pages: 1-31
Published on: March 20, 2002
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Electronic Journal of Probability. ISSN: 1083-6489 |
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