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 131
... continuous , then given any ( t , x ) , there is a Markov chain x ( s ) for st with initial data x ( t ) = x . The Dynkin formula ( 2.7 ) holds for any such that ( . , x ) and Pt ( , x ) are continuous . For Markov chains with an ...
... continuous , then given any ( t , x ) , there is a Markov chain x ( s ) for st with initial data x ( t ) = x . The Dynkin formula ( 2.7 ) holds for any such that ( . , x ) and Pt ( , x ) are continuous . For Markov chains with an ...
Page 154
... continuous on R + 1 . In ( 10.2 ) , G G where -G " is the generator of the semigroup T for a time - homogeneous controlled Markov process . Assume that there exists a dense subspace Do of the space of uniformly continuous , bounded ...
... continuous on R + 1 . In ( 10.2 ) , G G where -G " is the generator of the semigroup T for a time - homogeneous controlled Markov process . Assume that there exists a dense subspace Do of the space of uniformly continuous , bounded ...
Page 393
... continuous , with Lipschitz constant X : | g ( x ) − g ( y ) | ≤ \ | x − y | , \ x , y € K. - - For each ЄR ... continuous extension of g . If K is bounded , we obtain a bounded Lipschitz continuous extension ğ of g , by taking 9 = ağ ...
... continuous , with Lipschitz constant X : | g ( x ) − g ( y ) | ≤ \ | x − y | , \ x , y € K. - - For each ЄR ... continuous extension of g . If K is bounded , we obtain a bounded Lipschitz continuous extension ğ of g , by taking 9 = ağ ...
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