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 35
... calculus of variations problem in the sense that it satisfies the Euler equation . Every extremal satisfies the Euler differential equation ( ( 10.1 ) below ) . However , if x * ( · ) is minimizing , then additional conditions must hold ...
... calculus of variations problem in the sense that it satisfies the Euler equation . Every extremal satisfies the Euler differential equation ( ( 10.1 ) below ) . However , if x * ( · ) is minimizing , then additional conditions must hold ...
Page 51
... calculus of variations , this connection was known since Hamilton and Jacobi in the 19th century . It played an important role in Caratheodory's approach to calculus of varia- tions [ C ] . For a good , recent introduction to ...
... calculus of variations , this connection was known since Hamilton and Jacobi in the 19th century . It played an important role in Caratheodory's approach to calculus of varia- tions [ C ] . For a good , recent introduction to ...
Page 205
Wendell Helms Fleming, H. Mete Soner. IV.11 Stochastic calculus of variations In this section we consider a special class of problems , which are stochastic perturbations of certain problems in the classical calculus of variations of the ...
Wendell Helms Fleming, H. Mete Soner. IV.11 Stochastic calculus of variations In this section we consider a special class of problems , which are stochastic perturbations of certain problems in the classical calculus of variations of the ...
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