Stochastic Optimal Control for the Stochastic Heat Equation with Exponentially Growing Coefficients and with Control and Noise on a Subdomain |
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Authors: | Federica Masiero |
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Institution: | 1. Dipartimento di Matematica e Applicazioni , Università di Milano-Bicocca , Milano, Italy federica.masiero@unimib.it |
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Abstract: | Abstract We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain. |
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Keywords: | Backward stochastic differential equations Hamilton Jacobi Bellman equations Nonlinear stochastic heat equation Stochastic optimal control Stochastic processes in infinite dimensional spaces |
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