Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |
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Page 54
... discussion of discontinuous viscosity solutions is given Section VII.4 . The uniqueness of viscosity solutions is an important property which we discuss in Sections 9 and 14. We prove the uniqueness of viscosity solutions of a general ...
... discussion of discontinuous viscosity solutions is given Section VII.4 . The uniqueness of viscosity solutions is an important property which we discuss in Sections 9 and 14. We prove the uniqueness of viscosity solutions of a general ...
Page 55
... discuss the state constraint case in Section 12 as a first step toward a general for- mulation . We then extend our ... discussion of the connection between the adjoint variable and generalized gradients as defined in Section 8 below ...
... discuss the state constraint case in Section 12 as a first step toward a general for- mulation . We then extend our ... discussion of the connection between the adjoint variable and generalized gradients as defined in Section 8 below ...
Page 278
... discussion of change of proba- bility measure by conditioning is similar to that in Section 4 for Markov diffusions . For technical simplicity , let us again consider only finite - state Markov chains . Let x ( s ) be an irreducible ...
... discussion of change of proba- bility measure by conditioning is similar to that in Section 4 for Markov diffusions . For technical simplicity , let us again consider only finite - state Markov chains . Let x ( s ) be an irreducible ...
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Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |
Common terms and phrases
admissible control assume assumptions boundary condition boundary data bounded c₁ Cą(Q calculus of variations Chapter classical solution consider constant continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields