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 51
... method of dynamic programming was developed by Bellman during the same time period [ Be ] . For the Pontryagin ... method of characteristics for the Hamilton - Jacobi PDE , used in Section 10 , was called in calculus of variations the ...
... method of dynamic programming was developed by Bellman during the same time period [ Be ] . For the Pontryagin ... method of characteristics for the Hamilton - Jacobi PDE , used in Section 10 , was called in calculus of variations the ...
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 [ Kul ] . 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 [ Kul ] . 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 c₁ Cą(Q calculus of variations Chapter classical solution consider constant continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields