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 129
... called a backward evolution equation . If it has a solution ☀ € D ( A ) which also satisfies ( 2.11 ) , then by the Dynkin formula ( 2.7 ) with s = t1 ( 2.12 ) ( t , x ) = Etx { * l ( s , x ( 8 ) ) ds + $ ( x ( t ) ) } . t This gives a ...
... called a backward evolution equation . If it has a solution ☀ € D ( A ) which also satisfies ( 2.11 ) , then by the Dynkin formula ( 2.7 ) with s = t1 ( 2.12 ) ( t , x ) = Etx { * l ( s , x ( 8 ) ) ds + $ ( x ( t ) ) } . t This gives a ...
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 ...
Page 397
... called F. - progressively measurable if the map ( r , w ) → x ( r , w ) from [ t , s ] × N into Σ is B , × F , measurable , where B , = B ( [ t , s ] ) . The process is called F , -adapted if x ( s ,. ) is an F - measurable , Σ ...
... called F. - progressively measurable if the map ( r , w ) → x ( r , w ) from [ t , s ] × N into Σ is B , × F , measurable , where B , = B ( [ t , s ] ) . The process is called F , -adapted if x ( s ,. ) is an F - measurable , Σ ...
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