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 363
... finite difference quotients . Similarly , second - order partial derivatives are replaced by appropriate second - order finite - difference quotients ( Section 3. ) An important feature of Kushner's scheme is that the discretized HJB ...
... finite difference quotients . Similarly , second - order partial derivatives are replaced by appropriate second - order finite - difference quotients ( Section 3. ) An important feature of Kushner's scheme is that the discretized HJB ...
Page 374
... finite - difference approximations I We wish to show that the value function Vh obtained from the finite- difference scheme in Section 3 converges to the value function V for the controlled Markov diffusion as h → 0 . This has been ...
... finite - difference approximations I We wish to show that the value function Vh obtained from the finite- difference scheme in Section 3 converges to the value function V for the controlled Markov diffusion as h → 0 . This has been ...
Page 375
... finite - difference scheme ( 3.26 ) in Section 3. Then ( 4.7 ) = Σ ( 0.0 ) ] . Fr ( ) ( x ) = = min p ( x , y ) 4 ( y ) + hL ( x , y ) VEU Σ Then Ehh and p ( x , y ) is as in ( 3.25 ) , or ( 3.9 ) when n = 1. ( If a finite cutoff | x ...
... finite - difference scheme ( 3.26 ) in Section 3. Then ( 4.7 ) = Σ ( 0.0 ) ] . Fr ( ) ( x ) = = min p ( x , y ) 4 ( y ) + hL ( x , y ) VEU Σ Then Ehh and p ( x , y ) is as in ( 3.25 ) , or ( 3.9 ) when n = 1. ( If a finite cutoff | x ...
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