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 xi
... Finite fuel problem VIII.9 Historical remarks Finite - Difference Numerical Approximations 342 359 362 363 IX.1 Introduction 363 IX.2 IX.3 Controlled discrete - time Markov chains Finite - difference approximations to HJB equations 364 ...
... Finite fuel problem VIII.9 Historical remarks Finite - Difference Numerical Approximations 342 359 362 363 IX.1 Introduction 363 IX.2 IX.3 Controlled discrete - time Markov chains Finite - difference approximations to HJB equations 364 ...
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 ...
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 brownian motion C₁ Cą(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields