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 15
... unique solution satisfying the terminal condition ( 5.16 ) . We refer the reader to [ FR , p . 89 ] for more ... unique solution satisfying the initial condition x * ( t ) x . Thus there is a unique control u * ( · ) satisfying ( 5.17 ) ...
... unique solution satisfying the terminal condition ( 5.16 ) . We refer the reader to [ FR , p . 89 ] for more ... unique solution satisfying the initial condition x * ( t ) x . Thus there is a unique control u * ( · ) satisfying ( 5.17 ) ...
Page 17
... unique solution x ( · ) , and if ( 5.24 ) u ( s ) = u ( s , x ( s ) ) belongs to U ° ( t , x ) , then we call u an ... unique v * = u * ( s , y ) , this determines a candidate for the optimal feedback policy u * . If v * is not unique ...
... unique solution x ( · ) , and if ( 5.24 ) u ( s ) = u ( s , x ( s ) ) belongs to U ° ( t , x ) , then we call u an ... unique v * = u * ( s , y ) , this determines a candidate for the optimal feedback policy u * . If v * is not unique ...
Page 207
... unique v * = up ( t , x ) in UR for which the maximum is attained in ( 11.4R ) . Let us show that the control policy u belongs to the class C. For this purpose we prove the following : Lemma 11.1 . Let U CR " be compact and convex . Let ...
... unique v * = up ( t , x ) in UR for which the maximum is attained in ( 11.4R ) . Let us show that the control policy u belongs to the class C. For this purpose we prove the following : Lemma 11.1 . Let U CR " be compact and convex . Let ...
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