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 73
... subset of its domain , and We converges to W , uniformly on compact subsets of Q. Then W is a viscosity subsolution ( or a supersolution , respectively ) of the limiting equation . Proof . Let w E C∞ ( Q ) and ( t , x ) E Q be a strict ...
... subset of its domain , and We converges to W , uniformly on compact subsets of Q. Then W is a viscosity subsolution ( or a supersolution , respectively ) of the limiting equation . Proof . Let w E C∞ ( Q ) and ( t , x ) E Q be a strict ...
Page 229
... subset of Rd . Definition 5.1 . We say that EC ( G ) is semiconvex if for every bounded subset B of G there is a constant K ( B ) ≥ 0 such that , • B ( X ) = ˘ ( X ) + K ( B ) | X | 2 is convex on every convex subset of B. We say that ...
... subset of Rd . Definition 5.1 . We say that EC ( G ) is semiconvex if for every bounded subset B of G there is a constant K ( B ) ≥ 0 such that , • B ( X ) = ˘ ( X ) + K ( B ) | X | 2 is convex on every convex subset of B. We say that ...
Page 394
... subsets of Q * , hence on compact subsets of Q. Smoothing and semiconvexity . As in Section V.5 , let G be a compact subset of Rd and be a semiconvex function of G. Then there is K > 0 such that ( § ) + K || 2 is 394 Appendix C ...
... subsets of Q * , hence on compact subsets of Q. Smoothing and semiconvexity . As in Section V.5 , let G be a compact subset of Rd and be a semiconvex function of G. Then there is K > 0 such that ( § ) + K || 2 is 394 Appendix C ...
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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 brownian motion C₁ Cą(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields