A class of semilinear stochastic partial differential equations and their controls: Existence results
This paper concerns a class of similinear stochastic partial differential equations, of which the drift term is a second-order differential operator plus a nonlinearity, and the diffusion term is a first-order differential operator. When the nonlinearity is only continuous in the state, it is shown that there exist solutions of the equation provided that the Wiener process involved is one-dimensional. The existence of optimal relaxed controls for this class of equations is also proved. Our method is based on a group analysis of the first-order differential operator and a time change technique.
Year of publication: |
1993
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Authors: | Zhou, Xun Yu |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 44.1993, 1, p. 89-106
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Publisher: |
Elsevier |
Keywords: | semilinear stochastic partial differential equations group of operators time change compact embedding optimal relaxed controls |
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