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 28
... Remark 7.2 . A verification theorem entirely similar to Theorem 7.1 is true for the problem of control until the ... Remark 5.2 for the corresponding finite time horizon problem . Remark 7.2 will be used in the next example , 28 I ...
... Remark 7.2 . A verification theorem entirely similar to Theorem 7.1 is true for the problem of control until the ... Remark 5.2 for the corresponding finite time horizon problem . Remark 7.2 will be used in the next example , 28 I ...
Page 93
... Remark 9.2 . To analyze the interior maximum case , ( t , x ) , ( 3 , y ) Є Q , we used only the modulus of continuity , mw , of W. A symmetric argument can also be made by using only my . Hence the analysis of the interior max- imum ...
... Remark 9.2 . To analyze the interior maximum case , ( t , x ) , ( 3 , y ) Є Q , we used only the modulus of continuity , mw , of W. A symmetric argument can also be made by using only my . Hence the analysis of the interior max- imum ...
Page 210
... Remark 11.1 . Since VR V for R RK , formula ( 11.13 ) gives a = > stochastic representation for the gradient DV ( t , x ) . Remark 11.2 . In Theorem 11.1 we have taken ( x ) = 0 in ( 11.2 ) . To remove this restriction , let Є C3 ( R ...
... Remark 11.1 . Since VR V for R RK , formula ( 11.13 ) gives a = > stochastic representation for the gradient DV ( t , x ) . Remark 11.2 . In Theorem 11.1 we have taken ( x ) = 0 in ( 11.2 ) . To remove this restriction , let Є C3 ( R ...
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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 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