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 125
... Verification Theorem provides a solution to the problem . This tech- nique is applied to some illustrative examples in Section 8 , and for infinite time horizon models in Section 9. For deterministic control , corresponding Verification ...
... Verification Theorem provides a solution to the problem . This tech- nique is applied to some illustrative examples in Section 8 , and for infinite time horizon models in Section 9. For deterministic control , corresponding Verification ...
Page 167
... Verification Theorem 3.1 , a term q ( s , x * ( s ) , v ) W ( s , x * ( s ) ) must be added on the right side of formula ( 3.7 ) . To prove this form of the Verification Theorem , in the proof of Lemma 3.1 a Feynman- Kac formula ( see ...
... Verification Theorem 3.1 , a term q ( s , x * ( s ) , v ) W ( s , x * ( s ) ) must be added on the right side of formula ( 3.7 ) . To prove this form of the Verification Theorem , in the proof of Lemma 3.1 a Feynman- Kac formula ( see ...
Page 321
... Verification theorem loc We start with the definition of classical solutions of ( 2.7 ) . Let W1 , ( O ; R " ) be the set of all IR " -valued ... ( Verification ) Assume O is convex VIII . Singular Stochastic Control 321 Verification theorem.
... Verification theorem loc We start with the definition of classical solutions of ( 2.7 ) . Let W1 , ( O ; R " ) be the set of all IR " -valued ... ( Verification ) Assume O is convex VIII . Singular Stochastic Control 321 Verification theorem.
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