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 189
... difference quotients of V , and in Section 9 a one sided bound for certain second - order difference quotients . In case that V E C1,2 ( Qo ) these estimates provide corresponding estimates for partial derivatives of V. If V does not ...
... difference quotients of V , and in Section 9 a one sided bound for certain second - order difference quotients . In case that V E C1,2 ( Qo ) these estimates provide corresponding estimates for partial derivatives of V. If V does not ...
Page 363
... 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 equation ...
... 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 equation ...
Page 374
... 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 proved by ...
... 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 proved by ...
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