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Switched diffusion processes and systems of elliptic equations: A Dirichlet space approach. (English) Zbl 0807.47056

Summary: 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 generalized Skorohod decomposition for the reflecting switched diffusion process are obtained.

MSC:

47N20 Applications of operator theory to differential and integral equations
47F05 General theory of partial differential operators
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[1] Silverstein, Trans. Amer. Math. Soc. 244 pp 103– (1978)
[2] DOI: 10.1090/S0273-0979-1982-15041-8 · Zbl 0524.35002 · doi:10.1090/S0273-0979-1982-15041-8
[3] Protter, Maximum Principles in Differential Equations (1976)
[4] Eizenberg, Stochastics Stochastics Rep. 33 pp 111– (1990) · Zbl 0723.60095 · doi:10.1080/17442509008833669
[5] Edmunds, Spectral Theory and Differential Operators (1987) · Zbl 0628.47017
[6] Dellacherie, Probabilitiés et potential; Theories des Martingales (1980)
[7] DOI: 10.1007/BF01199246 · Zbl 0767.60074 · doi:10.1007/BF01199246
[8] Carrillo Menendez, C. R. Acad. Sci. Paris Sér. 1 Math. 302 pp 329– (1986)
[9] DOI: 10.1007/BF00538354 · Zbl 0299.60058 · doi:10.1007/BF00538354
[10] Bliedtner, Seminar on Potential Theory, II pp 1– (1970)
[11] DOI: 10.1007/BF01390195 · Zbl 0265.60074 · doi:10.1007/BF01390195
[12] DOI: 10.1214/aop/1176990437 · Zbl 0732.60090 · doi:10.1214/aop/1176990437
[13] Oshima, Lectures on Dirichlet spaces (1988)
[14] LeJan, Bull. Soc. Math. France 106 pp 61– (1978) · Zbl 0393.31008 · doi:10.24033/bsmf.1864
[15] Kunita, Proceedings of the International Conference on Functional Analysis and Related Topics pp 332– (1969)
[16] Kim, Osaka J. Math. 24 pp 331– (1987)
[17] Kato, Perturbation Theory for Linear Operators (1966) · Zbl 0148.12601
[18] Habetler, Proc. Sympos. Appl. Math. XI, Nuclear Reactor Theory pp 127– (1961)
[19] Fukushima, Dirichlet Forms and Markov Processes (1980)
[20] Freidlin, Functional Integration and Partial Differential Equations (1985) · Zbl 0568.60057 · doi:10.1515/9781400881598
[21] Eizenberg, Lecture Notes in Appl. Math. 27 pp 175– (1991)
[22] DOI: 10.1007/BF02570833 · Zbl 0727.35045 · doi:10.1007/BF02570833
[23] Skorohod, Asymptotic methods of the theory of Stochastic differential equations (1989)
[24] Silverstein, Symmetric Markov Processes (1974) · Zbl 0296.60038 · doi:10.1007/BFb0073683
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