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
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Page 136
... limit is called the heavy traffic limit . See Harrison [ Har ] concerning the use of heavy traffic limits for flow control . In other applications a diffusion limit is obtained for processes which are not Markov , or which are Markov on ...
... limit is called the heavy traffic limit . See Harrison [ Har ] concerning the use of heavy traffic limits for flow control . In other applications a diffusion limit is obtained for processes which are not Markov , or which are Markov on ...
Page 282
... limit point V * is equal to the smallest limit point V , and conse- quently the sequence Ve is uniformly convergent . Moreover the limit point V = V * = V , is both a viscosity subsolution and a viscosity supersolution of the limiting ...
... limit point V * is equal to the smallest limit point V , and conse- quently the sequence Ve is uniformly convergent . Moreover the limit point V = V * = V , is both a viscosity subsolution and a viscosity supersolution of the limiting ...
Page 285
... limit result , analogous to the law of large numbers . In particular , the limit of ( 2.1 ) should be related to a deterministic process . Indeed for € C1 ( Q ) the limit of ( G ) ( x ) , as ε tends to zero , is Gt ( x ) = H ( t , x ...
... limit result , analogous to the law of large numbers . In particular , the limit of ( 2.1 ) should be related to a deterministic process . Indeed for € C1 ( Q ) the limit of ( G ) ( x ) , as ε tends to zero , is Gt ( x ) = H ( t , x ...
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