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Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach

Published online by Cambridge University Press:  14 November 2011

Z. Q. Chen  and
Z. Zhao
Z. Q. Chen
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, U.S.A.
Z. Zhao
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
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Abstract

The switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a Dirichlet space approach and is applied to prove the existence theorem of the Cauchy initial problem for the system. A representation theorem for the solution of the Dirichlet boundary value problem and a generalised Skorohod decomposition for the reflecting switched diffusion process are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 673 - 701
Copyright
Copyright © Royal Society of Edinburgh 1994

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