A counter example for ergodic control theory in infinite dimensions

Mariko Arisawa, Hitoshi Ishii, Pierre Louis Lions

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present in this Note a simple example for an ergodic deterministic control problem in an infinite dimensional Hilbert space, for which classical results in finite dimensions fail. More precisely, this example shows that the convergence of value functions is not uniform in general as the discount factor goes to 0, or when the horizon of the problem goes to +∞.

Original languageEnglish
Pages (from-to)37-41
Number of pages5
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume325
Issue number1
Publication statusPublished - 1997 Jul
Externally publishedYes

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Ergodic Control
Discount Factor
Ergodic Theory
Infinite Dimensions
Control Theory
Value Function
Counterexample
Horizon
Control Problem
Hilbert space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A counter example for ergodic control theory in infinite dimensions. / Arisawa, Mariko; Ishii, Hitoshi; Lions, Pierre Louis.

In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 325, No. 1, 07.1997, p. 37-41.

Research output: Contribution to journalArticle

Arisawa, Mariko ; Ishii, Hitoshi ; Lions, Pierre Louis. / A counter example for ergodic control theory in infinite dimensions. In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 1997 ; Vol. 325, No. 1. pp. 37-41.
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