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 1
... problem is one of optimal control . In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ... Optimal Control Introduction.
... problem is one of optimal control . In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ... Optimal Control Introduction.
Page 51
... problem of calculus of variations . However , un- der some mild regularity ... optimal control problems considered in Sections 3-7 are of the type ... optimal control prob- lem , dynamic programming leads to the Hamilton - Jacobi ...
... problem of calculus of variations . However , un- der some mild regularity ... optimal control problems considered in Sections 3-7 are of the type ... optimal control prob- lem , dynamic programming leads to the Hamilton - Jacobi ...
Page 53
... optimal control problems . This method is equally useful in stochastic control , which will be formulated in Chapters III , IV and V. In both cases the value function of the control problem is defined to be the infimum of the payoff as ...
... optimal control problems . This method is equally useful in stochastic control , which will be formulated in Chapters III , IV and V. In both cases the value function of the control problem is defined to be the infimum of the payoff as ...
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 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