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 93
... proof of Theorem 9.1 , Ishii first showed that sup a ( t , x ; 3 , ÿ ) < ∞ . a > 0 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 a ( t , x ; 3 , ÿ ) < ∞ . a > 0 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 122
... proof of Crandall , Evans and Lions . More sophisticated uniqueness proofs are now available . See Ishii [ 14 ] and Crandall , Ishii and Lions [ CIL2 ] . These proofs in some cases provide a modulus of continuity for viscosity solutions ...
... proof of Crandall , Evans and Lions . More sophisticated uniqueness proofs are now available . See Ishii [ 14 ] and Crandall , Ishii and Lions [ CIL2 ] . These proofs in some cases provide a modulus of continuity for viscosity solutions ...
Page 299
... proof with attendant modifications yields a proof for Theorem II.14.1 . So in particular under the hypotheses of Theorems II.13.1 and II.14.1 , the value function is the unique continuous viscosity solution of I ( 5.3 ′ ) in Q and the ...
... proof with attendant modifications yields a proof for Theorem II.14.1 . So in particular under the hypotheses of Theorems II.13.1 and II.14.1 , the value function is the unique continuous viscosity solution of I ( 5.3 ′ ) in Q and the ...
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