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 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 333
... proves that P is a connected subset of IR " . Also the above characterization of P is the first step in studying the ... prove that the value function V is a viscosity solution of ( 2.7 ) in O. We assume that V E Cp ( O ) and it ...
... proves that P is a connected subset of IR " . Also the above characterization of P is the first step in studying the ... prove that the value function V is a viscosity solution of ( 2.7 ) in O. We assume that V E Cp ( O ) and it ...
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 do ( 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 do ( X ) be the set of ...
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