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 203
... convex function on R " . Convex- ity of V ( t ,. ) is equivalent to A2V ≥ 0. One then has a bound for A2V , which will imply the existence of generalized second derivatives V. , which are bounded on every compact set . Let us now ...
... convex function on R " . Convex- ity of V ( t ,. ) is equivalent to A2V ≥ 0. One then has a bound for A2V , which will imply the existence of generalized second derivatives V. , which are bounded on every compact set . Let us now ...
Page 229
... convex , bounded neighborhood of the origin . Since is semiconvex , there is K = K ( B ) < 0 such that $ ( X ) = 6 ( X ) + K | X | 2 is convex on B. Then the classical separation theorem for convex functions implies that there exists P ...
... convex , bounded neighborhood of the origin . Since is semiconvex , there is K = K ( B ) < 0 such that $ ( X ) = 6 ( X ) + K | X | 2 is convex on B. Then the classical separation theorem for convex functions implies that there exists P ...
Page 403
... convex and functional analysis and the area formula [ EG ] . More measure theoretic proofs are also possible . See for example Lemma 3.15 in [ J ] and Section 6.4 in [ EG ] . Suppose that C is a convex , closed subset of Rd with a ...
... convex and functional analysis and the area formula [ EG ] . More measure theoretic proofs are also possible . See for example Lemma 3.15 in [ J ] and Section 6.4 in [ EG ] . Suppose that C is a convex , closed subset of Rd with a ...
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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