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
... Section 4. In this abstract formulation the dynamic programming operator is viewed as the infinitesimal generator of a two parameter nonlinear semi- group satisfying ( 3.1 ) , ( 3.2 ) and ( 3.11 ) below . To define this semigroup , we ...
... Section 4. In this abstract formulation the dynamic programming operator is viewed as the infinitesimal generator of a two parameter nonlinear semi- group satisfying ( 3.1 ) , ( 3.2 ) and ( 3.11 ) below . To define this semigroup , we ...
Page 157
... Sections I.5 , III.8 and III.9 are proved . This is done for finite horizon problems in Section 3 , and for infinite horizon discounted problems in Section 5. Section 5 also provides illustrative examples . We saw in Chapters I and II ...
... Sections I.5 , III.8 and III.9 are proved . This is done for finite horizon problems in Section 3 , and for infinite horizon discounted problems in Section 5. Section 5 also provides illustrative examples . We saw in Chapters I and II ...
Page 282
... Section II.13 . In Section 6 below , we first give an extension of Definition II.13.1 and then show that V * and V. sat- isfy ( 2.4a ) in the viscosity sense . The combination of all these results yields several convergence results ...
... Section II.13 . In Section 6 below , we first give an extension of Definition II.13.1 and then show that V * and V. sat- isfy ( 2.4a ) in the viscosity sense . The combination of all these results yields several convergence results ...
Other editions - View all
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