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 47
Wendell Helms Fleming, H. Mete Soner. impose an additional condition on ( t , x ) , which will imply that the value function is smooth ( class C1 ) in some neighborhood of y * . This condition states that ( t , x ) is not a conjugate ...
Wendell Helms Fleming, H. Mete Soner. impose an additional condition on ( t , x ) , which will imply that the value function is smooth ( class C1 ) in some neighborhood of y * . This condition states that ( t , x ) is not a conjugate ...
Page 102
... condition satisfied by the value function when a state constraint is imposed . This condition plays an essential role in our discussion of boundary conditions when U ( t , x ) = U ° ( t ) but O ‡ R " . A general uniqueness result ...
... condition satisfied by the value function when a state constraint is imposed . This condition plays an essential role in our discussion of boundary conditions when U ( t , x ) = U ° ( t ) but O ‡ R " . A general uniqueness result ...
Page 256
... Condition ( 2.13 ) implies that V satisfies a polynomial growth condition IV ( 3.6 ) with m = 2. We need only to verify that u * € £ and use Corollary IV.3.1 . Since a , b C1 ( Qo ) and V E C1,2 ( Q ) , conditions IV ( 3.12 ) ( i ) and ...
... Condition ( 2.13 ) implies that V satisfies a polynomial growth condition IV ( 3.6 ) with m = 2. We need only to verify that u * € £ and use Corollary IV.3.1 . Since a , b C1 ( Qo ) and V E C1,2 ( Q ) , conditions IV ( 3.12 ) ( i ) and ...
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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 Cı(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