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 34
... called a Hamilton - Jacobi equation . If there are no constraints on x ( t1 ) , i.e. , M = R " , then ( 8.10 ) V ( t1 , x ) = √ ( x ) , x Є R " . Boundary conditions of type ( 8.10 ) , prescribing V at a fixed time t1 , are called ...
... called a Hamilton - Jacobi equation . If there are no constraints on x ( t1 ) , i.e. , M = R " , then ( 8.10 ) V ( t1 , x ) = √ ( x ) , x Є R " . Boundary conditions of type ( 8.10 ) , prescribing V at a fixed time t1 , are called ...
Page 129
... called a backward evolution equation . If it has a solution Є D ( A ) which also satisfies ( 2.11 ) , then by the Dynkin formula ( 2.7 ) with s = t1 ( 2.12 ) ( t , x ) = Etx { ƒ . " * £ ( s , x ( 9 ) ) ds + v ( x ( t , ) ) } . { ⁄ This ...
... called a backward evolution equation . If it has a solution Є D ( A ) which also satisfies ( 2.11 ) , then by the Dynkin formula ( 2.7 ) with s = t1 ( 2.12 ) ( t , x ) = Etx { ƒ . " * £ ( s , x ( 9 ) ) ds + v ( x ( t , ) ) } . { ⁄ This ...
Page 136
... 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 a higher ...
... 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 a higher ...
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 brownian motion C₁ Cı(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields