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 5
... formulation . A terminal time t1 will be fixed throughout . Let to < t1 and consider initial times t in the finite interval [ to , t1 ) . ( One could equally well take -∞ < t < t1 , but then certain assumptions in the problem formulation ...
... formulation . A terminal time t1 will be fixed throughout . Let to < t1 and consider initial times t in the finite interval [ to , t1 ) . ( One could equally well take -∞ < t < t1 , but then certain assumptions in the problem formulation ...
Page 53
... formulated in Chapters III , IV and V. In both cases the value function of the control problem is defined to be the ... formulation which they called viscosity solutions . Although the name " viscosity " refers to a certain relaxation ...
... formulated in Chapters III , IV and V. In both cases the value function of the control problem is defined to be the ... formulation which they called viscosity solutions . Although the name " viscosity " refers to a certain relaxation ...
Page 106
... formulation of the bound- ary condition ( 9.3a ) . We then verify that the value function satisfies this vis- cosity formulation . Also a continuity result for the value function is stated at the end of the section . First let us assume ...
... formulation of the bound- ary condition ( 9.3a ) . We then verify that the value function satisfies this vis- cosity formulation . Also a continuity result for the value function is stated at the end of the section . First let us assume ...
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 C¹(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