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 200
... uniformly bounded on every compact set B C Qo , Lemma 10.1 implies that AV tends weakly in Loc ( Qo ) to a limit y ... uniformly on compact sets to f , o , L as n → ∞o ; ( b ) the partial derivatives of fn , on with respect to t , xi ...
... uniformly bounded on every compact set B C Qo , Lemma 10.1 implies that AV tends weakly in Loc ( Qo ) to a limit y ... uniformly on compact sets to f , o , L as n → ∞o ; ( b ) the partial derivatives of fn , on with respect to t , xi ...
Page 202
... uniformly bounded on each compact set BC Qo since Aon = An – fn · D2 and AnVn , fn · DxVn are uniformly bounded on compact sets . The proof is then the same as for Lemma 10.3 . ᄆ Definition . Let W be locally Lipschitz on Qo . We call ...
... uniformly bounded on each compact set BC Qo since Aon = An – fn · D2 and AnVn , fn · DxVn are uniformly bounded on compact sets . The proof is then the same as for Lemma 10.3 . ᄆ Definition . Let W be locally Lipschitz on Qo . We call ...
Page 377
... uniformly for xr in any compact subset of R " . Theorem 4.1 . Let Vh be a solution to ( 4.1 ) and ( 4.2 ) . Assume that ( 4.3 ) - ( 4.6 ) and ( 4.11 ) hold . Then ( 4.12 ) lim Vh ( s , y ) = V ( t , x ) ( s , y ) → ( t , x ) h10 uniformly ...
... uniformly for xr in any compact subset of R " . Theorem 4.1 . Let Vh be a solution to ( 4.1 ) and ( 4.2 ) . Assume that ( 4.3 ) - ( 4.6 ) and ( 4.11 ) hold . Then ( 4.12 ) lim Vh ( s , y ) = V ( t , x ) ( s , y ) → ( t , x ) h10 uniformly ...
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