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 136
... 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 consider problems in which the ...
... 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 consider problems in which the ...
Page 137
... Markov process . Discontinuous Markov policies u must often be admitted , in order to obtain a policy u * which minimizes an expected cost criterion J of the type ( 6.5 ) below . This introduces additional mathematical complications ...
... Markov process . Discontinuous Markov policies u must often be admitted , in order to obtain a policy u * which minimizes an expected cost criterion J of the type ( 6.5 ) below . This introduces additional mathematical complications ...
Page 275
... Markov diffusion processes to other classes of Markov processes . These results are based mainly on Sheu [ Sh1 ] . Following the notation of Section III.2 , let A be the backward evolution operator of a Markov process x ( s ) , with ...
... Markov diffusion processes to other classes of Markov processes . These results are based mainly on Sheu [ Sh1 ] . Following the notation of Section III.2 , let A be the backward evolution operator of a Markov process x ( s ) , with ...
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