A counter example for ergodic control theory in infinite dimensions

Mariko Arisawa*, Hitoshi Ishii, Pierre Louis Lions

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number1
Publication statusPublished - 1997 Jul
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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