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
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
Page 64
... define the notion of viscosity solutions of the abstract dynamic programming equation ( 3.12 ) . This is a ... defined as in Definition 4.1 . But to have a meaningful theory { WE C ( [ to , ti ] × Σ ) : Wt ( t , x ) , ( G¿W ( t ...
... define the notion of viscosity solutions of the abstract dynamic programming equation ( 3.12 ) . This is a ... defined as in Definition 4.1 . But to have a meaningful theory { WE C ( [ to , ti ] × Σ ) : Wt ( t , x ) , ( G¿W ( t ...
Page 141
... defined in Section 6. ) In this section , we show that if W is a classical solution , then W ( t , x ) equals the minimum total expected cost among an appropriately defined class of admissible control systems . See Theorem 8.1 . The ...
... defined in Section 6. ) In this section , we show that if W is a classical solution , then W ( t , x ) equals the minimum total expected cost among an appropriately defined class of admissible control systems . See Theorem 8.1 . The ...
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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 C¹(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