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 54
... first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract discussion of viscosity solutions in Section 4. In this abstract formulation the dynamic programming operator is ...
... first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract discussion of viscosity solutions in Section 4. In this abstract formulation the dynamic programming operator is ...
Page 54
... first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract discussion of viscosity solutions in Section 4. In this abstract formulation the dynamic programming operator is ...
... first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract discussion of viscosity solutions in Section 4. In this abstract formulation the dynamic programming operator is ...
Page 122
... first given by Crandall and Lions [ CL1 ] for a general first - order partial differential equation . They also proved the uniqueness of viscosity solutions . Then equivalent definitions were pro- vided by Crandall , Evans and Lions ...
... first given by Crandall and Lions [ CL1 ] for a general first - order partial differential equation . They also proved the uniqueness of viscosity solutions . Then equivalent definitions were pro- vided by Crandall , Evans and Lions ...
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