Some Results on Bellman Equation in Hilbert Spaces

DOI10.1137/0323006zbMath0577.49020OpenAlexW2144819142MaRDI QIDQ3699493

Giuseppe Da Prato

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1137/0323006

zbMATH Keywords

Bellman equationHilbert spacenonlinear semigroup

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Dynamic programming in optimal control and differential games (49L20) Optimal stochastic control (93E20) Existence theories for problems in abstract spaces (49J27) Initial value problems for linear higher-order PDEs (35G10) Optimality conditions for problems involving randomness (49K45) Inner product spaces and their generalizations, Hilbert spaces (46C99) Higher-order parabolic equations (35K25)

Related Items (9)

Some results on parabolic evolution equations with infinitely many variables ⋮ Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: \(L^{2}_{\mu}\) approach ⋮ Robust control of parabolic stochastic partial differential equations under model uncertainty ⋮ Infinite-dimensional Hamilton-Jacobi-Bellman equations in gauss-sobolev spaces ⋮ Existence of optimal and \(\varepsilon\)-optimal controls for the stochastic Navier-Stokes equation ⋮ Smoothing properties of transition semigroups in hilbert spaces ⋮ Mild solutions of semilinear elliptic equations in Hilbert spaces ⋮ Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions ⋮ Dynamic programming for the stochastic Burgers equation

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