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 211
... proving regularity properties of value functions , such as the existence of AV in Theorem 10.1 . Krylov's estimate was proved for control problems on a fixed time interval [ t , t1 ] . Lions [ L3 ] proved corresponding estimates for ...
... proving regularity properties of value functions , such as the existence of AV in Theorem 10.1 . Krylov's estimate was proved for control problems on a fixed time interval [ t , t1 ] . Lions [ L3 ] proved corresponding estimates for ...
Page 251
... prove the dynamic programming principle by a space discretization . Their method requires the continuity of the value function . Borkar [ Bo ] proves the dy- namic programming by considering Markov policies . El Karoui et al . [ ENJ ] ...
... prove the dynamic programming principle by a space discretization . Their method requires the continuity of the value function . Borkar [ Bo ] proves the dy- namic programming by considering Markov policies . El Karoui et al . [ ENJ ] ...
Page 403
... prove that semiconvex functions are almost everywhere twice differentiable . This is a classical result due to ... prove the theorem for convex functions . We prove the main result in several steps . 1. Let ( X ) be the set of ...
... prove that semiconvex functions are almost everywhere twice differentiable . This is a classical result due to ... prove the theorem for convex functions . We prove the main result in several steps . 1. Let ( X ) be the set of ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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 C¹(Q calculus of variations Chapter classical solution consider constant convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields