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. |
From inside the book
Results 1-3 of 52
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 282
... viscosity subsolution and a viscosity supersolution of the limiting equation . The Barles - Perthame procedure requires a discussion of discontinuous viscosity sub- and supersolutions . In Definition 4.1 below , we give the def- inition ...
... viscosity subsolution and a viscosity supersolution of the limiting equation . The Barles - Perthame procedure requires a discussion of discontinuous viscosity sub- and supersolutions . In Definition 4.1 below , we give the def- inition ...
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 ...
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 Cą(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