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 55
... boundary and terminal con- ditions . This unique characterization of the value function is especially im- portant in ... condition satisfied by the value function . This issue of the boundary condition has been given a satisfactory ...
... boundary and terminal con- ditions . This unique characterization of the value function is especially im- portant in ... condition satisfied by the value function . This issue of the boundary condition has been given a satisfactory ...
Page 102
... variable p yields that the condition H1 ( t , x , D2V ( t , x ) ) · n ( x ) > 0 is equivalent to ( 12.4 ) , whenever H , exists . To obtain a weak formulation of ( 12.4 ) , 102 II . Viscosity Solutions Discussion of boundary conditions.
... variable p yields that the condition H1 ( t , x , D2V ( t , x ) ) · n ( x ) > 0 is equivalent to ( 12.4 ) , whenever H , exists . To obtain a weak formulation of ( 12.4 ) , 102 II . Viscosity Solutions Discussion of boundary conditions.
Page 106
Wendell Helms Fleming, H. Mete Soner. II.13 Discussion of boundary conditions Consider the deterministic optimal ... condition ( 9.3a ) is satisfied . However , in Example 2.3 we have shown that ( 9.3a ) is not always satisfied . In this ...
Wendell Helms Fleming, H. Mete Soner. II.13 Discussion of boundary conditions Consider the deterministic optimal ... condition ( 9.3a ) is satisfied . However , in Example 2.3 we have shown that ( 9.3a ) is not always satisfied . In this ...
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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