A class of semilinear stochastic partial differential equations and their controls: Existence results

Xun Yu Zhou

Stochastic Processes and their Applications, 1993, vol. 44, issue 1, 89-106

Abstract: 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.

Keywords: semilinear; stochastic; partial; differential; equations; group; of; operators; time; change; compact; embedding; optimal; relaxed; controls (search for similar items in EconPapers)
Date: 1993
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