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 270
... risk sensitive optimal control of Markov diffusions is concerned with the problems in which the functions b , o , q also depend on a control . Instead of the linear PDE ( 6.3 ) , p then satisfies a Hamilton - Jacobi - Bellman PDE ...
... risk sensitive optimal control of Markov diffusions is concerned with the problems in which the functions b , o , q also depend on a control . Instead of the linear PDE ( 6.3 ) , p then satisfies a Hamilton - Jacobi - Bellman PDE ...
Page 423
... Risk - sensitive Optimal Control , Wiley , New York , 1990 . [ Wh2 ] P. Whittle , A risk sensitive maximum principle , Syst . Control Lett . , 15 ( 1990 ) 183-192 . [ WCM ] S. A. Williams , P.-L. Chow and J.-L. Menaldi , Regularity of ...
... Risk - sensitive Optimal Control , Wiley , New York , 1990 . [ Wh2 ] P. Whittle , A risk sensitive maximum principle , Syst . Control Lett . , 15 ( 1990 ) 183-192 . [ WCM ] S. A. Williams , P.-L. Chow and J.-L. Menaldi , Regularity of ...
Page 427
... risk sensitive control , 270 running cost , 3 , 6 , 129 , 137 Schrodinger's equation , 270 semiclassical limit , 270 semiconcave function , 83 , 197 , 229 semicontinuous envelope upper , 287 lower , 287 semiconvex function , 83 , 229 ...
... risk sensitive control , 270 running cost , 3 , 6 , 129 , 137 Schrodinger's equation , 270 semiclassical limit , 270 semiconcave function , 83 , 197 , 229 semicontinuous envelope upper , 287 lower , 287 semiconvex function , 83 , 229 ...
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 Cą(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