Invariant Measure for Diffusions with Jumps |
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Authors: | J -L Menaldi M Robin |
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Institution: | (1) Department of Mathematics, Wayne State University, MI 48202, USA jlm@math.wayne.edu , US;(2) European Organization for Nuclear Research, CERN, Geneva 23, Switzerland CH-1211 maurice_robin@macmail.cern.ch , CH |
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Abstract: | Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This
integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key
result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients
are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions
to the ergodic linear equation are established.
Accepted 24 February 1998 |
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Keywords: | , Jump diffusion, Interior Dirichlet problem, Exterior Dirichlet problem, Ergodic optimal control, Green function,,,,,,Girsanov transformation, Doeblin condition, AMS Classification, Primary 35J25, 60J60, 60J75, Secondary 45K05, 46N20, 49A60,,,,,,93D05, 93E20, |
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