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. |
From inside the book
Results 1-3 of 63
Page 35
... corresponding calculus of variations problem . We shall return to this point in Section 10 . Example 8.1 . Suppose that L = L ( v ) . Then it suffices to consider linear functions x ( · ) in ( 8.2 ) . Indeed , given any Lipschitz ...
... corresponding calculus of variations problem . We shall return to this point in Section 10 . Example 8.1 . Suppose that L = L ( v ) . Then it suffices to consider linear functions x ( · ) in ( 8.2 ) . Indeed , given any Lipschitz ...
Page 160
... corresponding candidate VAS for the " value function . " Given v , u ( · ) € At , and initial data ( 2.4 ) , let x ( ) be the corresponding solution of ( 2.1 ) . Then the system π = ( N , { F } , P , x ( · ) , u ( · ) ) is admissible ...
... corresponding candidate VAS for the " value function . " Given v , u ( · ) € At , and initial data ( 2.4 ) , let x ( ) be the corresponding solution of ( 2.1 ) . Then the system π = ( N , { F } , P , x ( · ) , u ( · ) ) is admissible ...
Page 215
... corresponding result in Section IV.7 . However , additional assumptions will be needed to ensure continuity of the value function V on Q. Let us begin by considering an auxiliary control problem , in which the running cost L and ...
... corresponding result in Section IV.7 . However , additional assumptions will be needed to ensure continuity of the value function V on Q. Let us begin by considering an auxiliary control problem , in which the running cost L and ...
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