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 vii
... tion . The theory of viscosity solutions , first introduced by M. G. Crandall and P.-L. Lions , provides a convenient framework in which to study HJB equations . Typically , the value function is not smooth enough to satisfy the HJB ...
... tion . The theory of viscosity solutions , first introduced by M. G. Crandall and P.-L. Lions , provides a convenient framework in which to study HJB equations . Typically , the value function is not smooth enough to satisfy the HJB ...
Page 11
... tion satisfied by the value function . In general , however , the value function is not differentiable . In that case a notion of " weak ” solutions to this equa- tion is needed . This will be the subject of Chapter II . After formally ...
... tion satisfied by the value function . In general , however , the value function is not differentiable . In that case a notion of " weak ” solutions to this equa- tion is needed . This will be the subject of Chapter II . After formally ...
Page 197
... tion on IR " ( see Remark II.8.1 for the definition ) . IV.10 Generalized subsolutions and solutions Let us now use the estimates for difference quotients in Sections 8 and 9 to describe V as a generalized solution to the HJB equation ...
... tion on IR " ( see Remark II.8.1 for the definition ) . IV.10 Generalized subsolutions and solutions Let us now use the estimates for difference quotients in Sections 8 and 9 to describe V as a generalized solution to the HJB equation ...
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