### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Comptes Rendus de l'Academie des Sciences - Series I: Mathematics*,

*325*(1), 37-41.

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

Research output: Contribution to journal › Article

*Comptes Rendus de l'Academie des Sciences - Series I: Mathematics*, vol. 325, no. 1, pp. 37-41.

}

TY - JOUR

T1 - A counter example for ergodic control theory in infinite dimensions

AU - Arisawa, Mariko

AU - Ishii, Hitoshi

AU - Lions, Pierre Louis

PY - 1997/7

Y1 - 1997/7

N2 - 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 +∞.

AB - 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 +∞.

UR - http://www.scopus.com/inward/record.url?scp=0031185165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031185165&partnerID=8YFLogxK

M3 - Article

VL - 325

SP - 37

EP - 41

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 1

ER -