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 16
... ( Theorem II.10.2 ) . Boundary conditions are discussed further in Section II.13 . Theorem 5.2 . Let WE C1 ( Q ) ... proof of Theorem 5.2 is almost the same as for Theorem 5.1 . In ( 5.8 ) the integral is now from t to the exit time 7 , and ...
... ( Theorem II.10.2 ) . Boundary conditions are discussed further in Section II.13 . Theorem 5.2 . Let WE C1 ( Q ) ... proof of Theorem 5.2 is almost the same as for Theorem 5.1 . In ( 5.8 ) the integral is now from t to the exit time 7 , and ...
Page 93
... proof of Theorem 9.1 , Ishii first showed that sup Þ 。( t , x ; 3 , ÿ ) < ∞ . a > 0 α Then repeating the proof of Theorem 9.1 he completed his proof of unique- ness . ( See Theorems 2.1 , 2.3 in [ 13 ] and Section 5.D in [ CIL1 ] ...
... proof of Theorem 9.1 , Ishii first showed that sup Þ 。( t , x ; 3 , ÿ ) < ∞ . a > 0 α Then repeating the proof of Theorem 9.1 he completed his proof of unique- ness . ( See Theorems 2.1 , 2.3 in [ 13 ] and Section 5.D in [ CIL1 ] ...
Page 300
... proof of Theorem 8.1 , but use the above estimate instead of ( 8.1 ) . Combining Theorem 7.1 , and Theorem 8.1 or 8.2 we obtain a conver- gence result for V. However the existence of a continuous or a Lipschitz continuous viscosity ...
... proof of Theorem 8.1 , but use the above estimate instead of ( 8.1 ) . Combining Theorem 7.1 , and Theorem 8.1 or 8.2 we obtain a conver- gence result for V. However the existence of a continuous or a Lipschitz continuous viscosity ...
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