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August, 1985 A Classification of Diffusion Processes with Boundaries by their Invariant Measures
Ross Pinsky
Ann. Probab. 13(3): 693-697 (August, 1985). DOI: 10.1214/aop/1176992903

Abstract

Let $D$ be a connected, compact region in $R^d$. If $d = 1$, then for each nice probability measure $\mu$ on $D$ and diffusion coefficient $a$, there exists a unique drift such that $\mu$ is invariant for the resulting diffusion process with reflection at the boundary. For $d > 1$, there is no uniqueness. For each diffusion matrix $a$, reflection vector $J$, and nice probability measure $\mu$ on $D$, we classify the collection of drifts such that $\mu$ is invariant for the resulting diffusion process. We use the theory of the $I$-function and, in the course of things, answer a question about the $I$-function.

Citation

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Ross Pinsky. "A Classification of Diffusion Processes with Boundaries by their Invariant Measures." Ann. Probab. 13 (3) 693 - 697, August, 1985. https://doi.org/10.1214/aop/1176992903

Information

Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0582.60074
MathSciNet: MR799417
Digital Object Identifier: 10.1214/aop/1176992903

Subjects:
Primary: 60J60

Keywords: diffusion processes with boundaries , drifts , Invariant measures

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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