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
... Theorem 9.1 due to Ishii , which does not use the modulus of continuity of either function [ 14 ] , [ CIL2 ] . Extensions of Theorem 9.1 to unbounded solutions and Hamiltonians which do not satisfy ( 9.4 ) have been studied by Ishii ...
... Theorem 9.1 due to Ishii , which does not use the modulus of continuity of either function [ 14 ] , [ CIL2 ] . Extensions of Theorem 9.1 to unbounded solutions and Hamiltonians which do not satisfy ( 9.4 ) have been studied by Ishii ...
Page 147
... Theorem 9.1 is an immediate consequence of Lemma 9.1 . The control system π * is optimal in the class C1 . As in the finite horizon case ( Section 8 ) we may seek to find an optimal stationary Markov control policy u * such that ( 9.9 ) ...
... Theorem 9.1 is an immediate consequence of Lemma 9.1 . The control system π * is optimal in the class C1 . As in the finite horizon case ( Section 8 ) we may seek to find an optimal stationary Markov control policy u * such that ( 9.9 ) ...
Page 302
Wendell Helms Fleming, H. Mete Soner. Theorem 9.1 . Assume that the hypotheses of Theorem 8.1 or Theorem 8.2 or Theorem 8.3 or Theorem 8.4 are satisfied . Then Ve converges uni- formly to the unique solution of ( 2.3 ) - ( 2.4 ) on Q or ...
Wendell Helms Fleming, H. Mete Soner. Theorem 9.1 . Assume that the hypotheses of Theorem 8.1 or Theorem 8.2 or Theorem 8.3 or Theorem 8.4 are satisfied . Then Ve converges uni- formly to the unique solution of ( 2.3 ) - ( 2.4 ) on Q or ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
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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