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
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
Page 54
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
... define this semigroup , we view a given function as the terminal data to our optimal control problem . Then the value function with terminal data is defined to be the evaluation of the semigroup at . In this formalism , the semigroup ...
Page 64
... define the notion of viscosity solutions of the abstract dynamic programming equation ( 3.12 ) . This is a ... defined as in Definition 4.1 . But to have a meaningful theory of viscosity solutions , the notion of a viscosity ...
... define the notion of viscosity solutions of the abstract dynamic programming equation ( 3.12 ) . This is a ... defined as in Definition 4.1 . But to have a meaningful theory of viscosity solutions , the notion of a viscosity ...
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