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 5
... fixed . At the opposite extreme , there is no restriction on x ( t1 ) if M = R " . - We will discuss calculus of variations problems in some detail in Sections 8 10. In the formulation in Section 8 , we allow the possibility that the fixed ...
... fixed . At the opposite extreme , there is no restriction on x ( t1 ) if M = R " . - We will discuss calculus of variations problems in some detail in Sections 8 10. In the formulation in Section 8 , we allow the possibility that the fixed ...
Page 159
... fixed initial data ( 2.4 ) x ( t ) = x , x R " . = From standard theory of stochastic differential equations with random co- efficients , ( 2.1 ) , ( 2.4 ) has a pathwise unique solution x ( s ) which is F- progressively measurable and ...
... fixed initial data ( 2.4 ) x ( t ) = x , x R " . = From standard theory of stochastic differential equations with random co- efficients , ( 2.1 ) , ( 2.4 ) has a pathwise unique solution x ( s ) which is F- progressively measurable and ...
Page 177
... Fixed finite time horizon problem : Preliminary estimates We will take Q = Qo = [ to , t1 ) × R " in the rest of this chapter . Thus , control occurs on a fixed finite interval [ t , t1 ] . Our goal is to study systematically the value ...
... Fixed finite time horizon problem : Preliminary estimates We will take Q = Qo = [ to , t1 ) × R " in the rest of this chapter . Thus , control occurs on a fixed finite interval [ t , t1 ] . Our goal is to study systematically the value ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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