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 4
Wendell Helms Fleming, H. Mete Soner. We require that u ( s ) € U , where U is a closed interval . For instance , if ... requiring x ( t ) = x where x IR " is given . For the Є right endpoint , let us fix t1 and require that 4 I ...
Wendell Helms Fleming, H. Mete Soner. We require that u ( s ) € U , where U is a closed interval . For instance , if ... requiring x ( t ) = x where x IR " is given . For the Є right endpoint , let us fix t1 and require that 4 I ...
Page 100
... require Ww at the extrema . In the above definition , however , we do not require this equality , but instead we use BW ( T ) both in ( 11.4 ) and ( 11.5 ) . This modification is discussed in detail in Remark 4.2 . Also , in the above ...
... require Ww at the extrema . In the above definition , however , we do not require this equality , but instead we use BW ( T ) both in ( 11.4 ) and ( 11.5 ) . This modification is discussed in detail in Remark 4.2 . Also , in the above ...
Page 103
... require neither V nor the boundary 00 to be differentiable . Definition 12.1 . We say that We C ( Q ) is a viscosity supersolution of I ( 5.3 ' ) on [ to , t1 ) x Ō if , for each w E C∞ ( Q ) , ( 12.5 ) მ w ( t , x ) + H ( t , x , Dxw ...
... require neither V nor the boundary 00 to be differentiable . Definition 12.1 . We say that We C ( Q ) is a viscosity supersolution of I ( 5.3 ' ) on [ to , t1 ) x Ō if , for each w E C∞ ( Q ) , ( 12.5 ) მ w ( t , x ) + H ( t , x , Dxw ...
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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