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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Results 1-3 of 47
Page 173
... apply Corollary 5.1 in the special case L ( x , v ) = 1 , g ( x ) = 0 , ẞ = 0. Let O be bounded and U 0 , ß compact . Moreover , assume the uniform ellipticity condition ( 5.10 ) , which implies < ∞ with probability 1. Let J ( x ; u ) ...
... apply Corollary 5.1 in the special case L ( x , v ) = 1 , g ( x ) = 0 , ẞ = 0. Let O be bounded and U 0 , ß compact . Moreover , assume the uniform ellipticity condition ( 5.10 ) , which implies < ∞ with probability 1. Let J ( x ; u ) ...
Page 282
... apply these comparison results to V * and V. , we need to show that V * and V. satisfy the same terminal and ... application the con- vergence of Ve follows immediately from the results of Section 7 , if Ve is uniformly bounded in ɛ ...
... apply these comparison results to V * and V. , we need to show that V * and V. satisfy the same terminal and ... application the con- vergence of Ve follows immediately from the results of Section 7 , if Ve is uniformly bounded in ɛ ...
Page 301
... apply to this case . The conditions I ( 3.11 ) and II ( 13.6 ) have to be used once again to verify the hypotheses of theorem of Barles and Perthame or Ishii . Remark 8.2 . Under the hypotheses of Theorem II.13.1 ( b ) the two exit time ...
... apply to this case . The conditions I ( 3.11 ) and II ( 13.6 ) have to be used once again to verify the hypotheses of theorem of Barles and Perthame or Ishii . Remark 8.2 . Under the hypotheses of Theorem II.13.1 ( b ) the two exit time ...
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