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 98
... Lipschitz continuous viscosity solution of the dynamic programming equation I ( 5.3 ′ ) in Q , satisfying the boundary conditions ( 9.3 ) . In particular the nonlinear partial differential equation I ( 10.8 ) has a unique Lipschitz ...
... Lipschitz continuous viscosity solution of the dynamic programming equation I ( 5.3 ′ ) in Q , satisfying the boundary conditions ( 9.3 ) . In particular the nonlinear partial differential equation I ( 10.8 ) has a unique Lipschitz ...
Page 299
... continuous on Q. However the existence of a continuous solution satisfying the boundary con- dition is not assumed ... Lipschitz continuous on Q and V is nonnegative and Lipschitz continuous on Q with y ( t , x ) = 0 for all ( t , x ) Є ...
... continuous on Q. However the existence of a continuous solution satisfying the boundary con- dition is not assumed ... Lipschitz continuous on Q and V is nonnegative and Lipschitz continuous on Q with y ( t , x ) = 0 for all ( t , x ) Є ...
Page 393
Wendell Helms Fleming, H. Mete Soner. Appendix C Extension of Lipschitz Continuous Functions ; Smoothing In Sections VI.2 and VI.5 we used a result about Lipschitz continuous extensions of functions . Let KCR " and let g : K → Rm be ...
Wendell Helms Fleming, H. Mete Soner. Appendix C Extension of Lipschitz Continuous Functions ; Smoothing In Sections VI.2 and VI.5 we used a result about Lipschitz continuous extensions of functions . Let KCR " and let g : K → Rm be ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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