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 125
Wendell Helms Fleming, H. Mete Soner. III Optimal Control of Markov Processes : Classical Solutions III.1 Introduction The purpose of this chapter is to give a concise , nontechnical introduction to optimal stochastic control for Markov ...
Wendell Helms Fleming, H. Mete Soner. III Optimal Control of Markov Processes : Classical Solutions III.1 Introduction The purpose of this chapter is to give a concise , nontechnical introduction to optimal stochastic control for Markov ...
Page 133
... Markov process with state space Σ1 ; and -G2 generates the " parameter process " z ( s ) with state space Σ2 . Example ( c ) can be ... Processes : Classical Solutions 133 Markov diffusion processes on R"; stochastic differential equations.
... Markov process with state space Σ1 ; and -G2 generates the " parameter process " z ( s ) with state space Σ2 . Example ( c ) can be ... Processes : Classical Solutions 133 Markov diffusion processes on R"; stochastic differential equations.
Page 136
... processes which are not Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now ...
... processes which are not Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now ...
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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