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 366
... method is closely related to Newton's method for solving nonlinear equations [ Bs , p . 236 ] . For refinements of these methods for computing the value function and illustrative examples , we refer to [ Bs , Chap . 5 ] . IX.3 Finite ...
... method is closely related to Newton's method for solving nonlinear equations [ Bs , p . 236 ] . For refinements of these methods for computing the value function and illustrative examples , we refer to [ Bs , Chap . 5 ] . IX.3 Finite ...
Page 374
... methods . Later , another method to show convergence of Vh to V by vis- cosity solution techniques was introduced by Barles and Souganidis [ BS ] . This method is the one which we will follow . Both Kushner's stochastic control method ...
... methods . Later , another method to show convergence of Vh to V by vis- cosity solution techniques was introduced by Barles and Souganidis [ BS ] . This method is the one which we will follow . Both Kushner's stochastic control method ...
Page 388
... method used in this chapter is due to Kush- ner [ Ku1 ] . We have given only a concise introduction to the topic , with convergence proofs based on viscosity solution methods following Barles and Souganidis [ BS ] . Kushner - Dupuis ...
... method used in this chapter is due to Kush- ner [ Ku1 ] . We have given only a concise introduction to the topic , with convergence proofs based on viscosity solution methods following Barles and Souganidis [ BS ] . Kushner - Dupuis ...
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