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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Results 1-3 of 48
Page 188
... terminal data y = 0. For nonzero terminal data , the following extension of Theorem 7.1 holds . Corollary 7.1 . Assume ( 6.1 ) , ( 6.3 ) , and that is bounded and uniformly continuous . Then the conclusions of Theorem 7.1 are true ...
... terminal data y = 0. For nonzero terminal data , the following extension of Theorem 7.1 holds . Corollary 7.1 . Assume ( 6.1 ) , ( 6.3 ) , and that is bounded and uniformly continuous . Then the conclusions of Theorem 7.1 are true ...
Page 282
... terminal and boundary conditions . In Section 5 we show that V * and V. pointwise satisfy the terminal data ( 2.4b ) . The discussion of the lateral boundary data is more delicate as V * and V. satisfy ( 2.4a ) only in the viscosity ...
... terminal and boundary conditions . In Section 5 we show that V * and V. pointwise satisfy the terminal data ( 2.4b ) . The discussion of the lateral boundary data is more delicate as V * and V. satisfy ( 2.4a ) only in the viscosity ...
Page 377
... terminal data ( 4.2 ) in a uniform way : ( 4.11 ) lim Vh ( s , y ) = u ( x ) ( 8 , y ) → ( t1 , x ) h10 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 ) ...
... terminal data ( 4.2 ) in a uniform way : ( 4.11 ) lim Vh ( s , y ) = u ( x ) ( 8 , y ) → ( t1 , x ) h10 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 ) ...
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