### 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 language | English |
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Pages (from-to) | 37-41 |

Number of pages | 5 |

Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |

Volume | 325 |

Issue number | 1 |

Publication status | Published - 1997 Jul |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Arisawa, M., Ishii, H., & Lions, P. L. (1997). A counter example for ergodic control theory in infinite dimensions.

*Comptes Rendus de l'Academie des Sciences - Series I: Mathematics*,*325*(1), 37-41.