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 44
... satisfies ( 9.2 ) . At the end of the section , we will consider an application to first - order nonlinear PDEs , in which H rather than L is given . The idea in this application is to introduce the calculus of variations problem in ...
... satisfies ( 9.2 ) . At the end of the section , we will consider an application to first - order nonlinear PDEs , in which H rather than L is given . The idea in this application is to introduce the calculus of variations problem in ...
Page 107
... satisfies ( 13.1 ) . However , in Definition 13.1 we have used a weaker inequality ( 13.4 ) . So if we were only interested in dynamic programming equation I ( 5.3 ) we could replace ( 13.4 ) by ( 13.1 ) . But , when the Hamiltonian H ...
... satisfies ( 13.1 ) . However , in Definition 13.1 we have used a weaker inequality ( 13.4 ) . So if we were only interested in dynamic programming equation I ( 5.3 ) we could replace ( 13.4 ) by ( 13.1 ) . But , when the Hamiltonian H ...
Page 108
... satisfies ( 9.4 ) . We also assume that the boundary of O satisfies a regularity condition : there are ɛo , r > 0 and an R - valued , bounded , uniformly continuous map of Ō satisfying ( 14.1 ) B ( x + ɛî ( x ) , rɛ ) CO , Vx € 0 , ɛ ...
... satisfies ( 9.4 ) . We also assume that the boundary of O satisfies a regularity condition : there are ɛo , r > 0 and an R - valued , bounded , uniformly continuous map of Ō satisfying ( 14.1 ) B ( x + ɛî ( x ) , rɛ ) CO , Vx € 0 , ɛ ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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