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arXiv · 2105.05194

Peng's Maximum Principle for Stochastic Partial Differential Equations

Wilhelm Stannat·Lukas Wessels
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Abstract

We extend Peng's maximum principle for semilinear stochastic partial differential equations (SPDEs) in one space-dimension with non-convex control domains and control-dependent diffusion coefficients to the case of general cost functionals with Nemytskii-type coefficients. Our analysis is based on a new approach to the characterization of the second order adjoint state as the solution of a function-valued backward SPDE.

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Wilhelm Stannat, Lukas Wessels. 2021-05-11. Peng's Maximum Principle for Stochastic Partial Differential Equations. https://doi.org/10.1137/20m1368057

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