Stationary Hamilton--Jacobi Equations in Hilbert Spaces and Applications to a Stochastic Optimal Control Problem

DOI10.1137/S0363012999359949zbMath0992.60066MaRDI QIDQ2753231

Sandra Cerrai

Publication date: 29 October 2001

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

zbMATH Keywords

stochastic reaction-diffusion systemsinfinite horizon stochastic control problemsstationary Hamilton-Jacobi-Bellman equations in infinite dimension

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Optimal stochastic control (93E20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Transition functions, generators and resolvents (60J35)

Related Items (11)

Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula ⋮ On Stochastic Ergodic Control in Infinite Dimensions ⋮ Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: \(L^{2}_{\mu}\) approach ⋮ The existence and exponential behavior of solutions to time fractional stochastic delay evolution inclusions with nonlinear multiplicative noise and fractional noise ⋮ Robust control of parabolic stochastic partial differential equations under model uncertainty ⋮ HJB Equations in Infinite Dimension and Optimal Control of Stochastic Evolution Equations Via Generalized Fukushima Decomposition ⋮ Optimal control of path-dependent McKean-Vlasov SDEs in infinite-dimension ⋮ A Functional Analytic Approach to Infinite Dimensional Stochastic Linear Systems ⋮ DGM: a deep learning algorithm for solving partial differential equations ⋮ Asymptotic behaviour of stochastic quasi dissipative systems ⋮ Mild solutions of semilinear elliptic equations in Hilbert spaces

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