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 53
... value function of the control problem is defined to be the infimum of the payoff as a function of the ini- tial data . When the value function is smooth enough , it solves a nonlinear equation which we call the dynamic programing ...
... value function of the control problem is defined to be the infimum of the payoff as a function of the ini- tial data . When the value function is smooth enough , it solves a nonlinear equation which we call the dynamic programing ...
Page 55
Wendell Helms Fleming, H. Mete Soner. however , the value function is the unique viscosity solution of the dynamic programming equation satisfying appropriate boundary and terminal con- ditions . This unique characterization of the value ...
Wendell Helms Fleming, H. Mete Soner. however , the value function is the unique viscosity solution of the dynamic programming equation satisfying appropriate boundary and terminal con- ditions . This unique characterization of the value ...
Page 109
... value function V is bounded , uniformly continuous and V ( t1 , x ) = W ( t1 , x ) . Hence , in this case , the value function is the unique constrained viscosity solutions of I ( 5.3 ′ ) satisfying the terminal condition ( 9.3b ) ...
... value function V is bounded , uniformly continuous and V ( t1 , x ) = W ( t1 , x ) . Hence , in this case , the value function is the unique constrained viscosity solutions of I ( 5.3 ′ ) satisfying the terminal condition ( 9.3b ) ...
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