A uniform Tauberian theorem in optimal control
Oliu-Barton, Miquel; Vigeral, Guillaume (2012), A uniform Tauberian theorem in optimal control, in Pierre Cardialiguet, Ross Cressman, Advances in Dynamic Games Theory, Applications, and Numerical Methods for Differential and Stochastic Games, Annals of the International Society of Dynamic Games vol 12 : Advances in Dynamic Games, p. 199-215. 10.1007/978-0-8176-8355-9_10
Book titleAdvances in Dynamic Games Theory, Applications, and Numerical Methods for Differential and Stochastic Games
Book authorPierre Cardialiguet, Ross Cressman
MetadataShow full item record
Abstract (EN)In an optimal control framework, we consider the value VT(x) of the problem starting from state x with finite horizon T, as well as the value Wλ(x) of the λ-discounted problem starting from x. We prove that uniform convergence (on the set of states) of the values VT(⋅) as T tends to infinity is equivalent to uniform convergence of the values Wλ(⋅) as λ tends to 0, and that the limits are identical. An example is also provided to show that the result does not hold for pointwise convergence. This work is an extension, using similar techniques, of a related result by Lehrer and Sorin in a discrete-time framework.
Subjects / KeywordsTauberian theorem; Optimal control; Asymptotic value; Game theory
Showing items related by title and author.