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 359 IX IX.1 Introduction IX.2 IX.3 VIII.9 Historical remarks Finite - Difference Numerical Approximations Controlled discrete - time Markov chains Finite - difference approximations to HJB equations 362 363 363 364 ...
... Finite fuel problem 359 IX IX.1 Introduction IX.2 IX.3 VIII.9 Historical remarks Finite - Difference Numerical Approximations Controlled discrete - time Markov chains Finite - difference approximations to HJB equations 362 363 363 364 ...
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 ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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 C¹(Q calculus of variations Chapter classical solution consider constant convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields