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
... solution to the dynamic programming equation , with appropriate terminal data at a final time t1 , then a Verification Theorem provides a solution to the problem . This tech- nique is applied to some ... Classical Solutions Introduction.
... solution to the dynamic programming equation , with appropriate terminal data at a final time t1 , then a Verification Theorem provides a solution to the problem . This tech- nique is applied to some ... Classical Solutions Introduction.
Page 141
... 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 proof is quite simple , but the assumption that W is a classical ...
... 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 proof is quite simple , but the assumption that W is a classical ...
Page 157
... classical " solution . Verification Theorems in the same spirit as those in 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 ...
... classical " solution . Verification Theorems in the same spirit as those in 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 ...
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 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