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 OR " . A general uniqueness result covering ...
... 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 OR " . A general uniqueness result covering ...
Page 106
... condition ( 9.3a ) is satisfied . However , in Example 2.3 we have shown that ( 9.3a ) is not always satisfied . In this section we will derive a weak ( viscosity ) formulation of the bound- ary condition ( 9.3a ) . We then verify that ...
... condition ( 9.3a ) is satisfied . However , in Example 2.3 we have shown that ( 9.3a ) is not always satisfied . In this section we will derive a weak ( viscosity ) formulation of the bound- ary condition ( 9.3a ) . We then verify that ...
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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 brownian motion C₁ Cą(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