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 20
... Lipschitz function is differentiable at almost all points ( t , x ) Є Q. Definition . W is a generalized solution to the dynamic programming equation in Q if W is locally Lipschitz and satisfies ( 5.3 ) for almost all ( t , x ) E Q ...
... Lipschitz function is differentiable at almost all points ( t , x ) Є Q. Definition . W is a generalized solution to the dynamic programming equation in Q if W is locally Lipschitz and satisfies ( 5.3 ) for almost all ( t , x ) E Q ...
Page 299
... Lipschitz continuous on Q and V is nonnegative and Lipschitz continuous on Q with y ( t , x ) = 0 for all ( t , x ) Є [ to , t1 ] × 20. Then Proposition II.10.1 implies that the value function is Lipschitz continuous on Q. Our next ...
... Lipschitz continuous on Q and V is nonnegative and Lipschitz continuous on Q with y ( t , x ) = 0 for all ( t , x ) Є [ to , t1 ] × 20. Then Proposition II.10.1 implies that the value function is Lipschitz continuous on Q. Our next ...
Page 393
... Lipschitz continuous extensions of functions . Let KCR " and let g : K → Rm be Lipschitz continuous , with Lipschitz constant X : | g ( x ) − g ( y ) | ≤ \ | x − y | , \ x , y € K. - For each x ЄR " , let ( C.1 ) If xEK , y ЄK ...
... Lipschitz continuous extensions of functions . Let KCR " and let g : K → Rm be Lipschitz continuous , with Lipschitz constant X : | g ( x ) − g ( y ) | ≤ \ | x − y | , \ x , y € K. - For each x ЄR " , let ( C.1 ) If xEK , y ЄK ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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 convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields