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 69
... viscosity subsolution of ( 3.12 ) in Q. The supersolution property of V is proved exactly the same way as the subsolution property . We close this section by showing that the notion of viscosity solution is consistent with the notion of ...
... viscosity subsolution of ( 3.12 ) in Q. The supersolution property of V is proved exactly the same way as the subsolution property . We close this section by showing that the notion of viscosity solution is consistent with the notion of ...
Page 292
... solution of ( 2.3 ) and ( 2.4a ) if it is both a viscosity subsolution and a viscosity supersolution of ( 2.3 ) and ( 2.4a ) . The above definition is very similar to the definition given in Section II.13 . In the case of a subsolution ...
... solution of ( 2.3 ) and ( 2.4a ) if it is both a viscosity subsolution and a viscosity supersolution of ( 2.3 ) and ( 2.4a ) . The above definition is very similar to the definition given in Section II.13 . In the case of a subsolution ...
Page 293
... viscosity subsolution of ( 2.3 ) , ( 2.4a ) , in the sense of Definition 6.1 , and a pointwise subsolution of ( 2.4b ) , i.e. , ( W ) * ( t1 , x ) ≤ ( x ) for EŌ . In the sequel we call any such function a viscosity subsolution of ...
... viscosity subsolution of ( 2.3 ) , ( 2.4a ) , in the sense of Definition 6.1 , and a pointwise subsolution of ( 2.4b ) , i.e. , ( W ) * ( t1 , x ) ≤ ( x ) for EŌ . In the sequel we call any such function a viscosity subsolution of ...
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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