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 IR " . Convex- ity of V ( t ,. ) is equivalent to △ 2V ≥ 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 IR " . Convex- ity of V ( t ,. ) is equivalent to △ 2V ≥ 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 ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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