### Abstract

In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.

Original language | English |
---|---|

Pages (from-to) | 173-183 |

Number of pages | 11 |

Journal | Electronic Communications in Probability |

Volume | 12 |

Publication status | Published - 2007 May 16 |

Externally published | Yes |

### Fingerprint

### Keywords

- Concentration
- Large deviation principle
- Minimizers
- Pinned wiener measure
- Scaling limit

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**Dichotomy in a scaling limit under wiener measure with density.** / Funaki, Tadahisa.

Research output: Contribution to journal › Article

*Electronic Communications in Probability*, vol. 12, pp. 173-183.

}

TY - JOUR

T1 - Dichotomy in a scaling limit under wiener measure with density

AU - Funaki, Tadahisa

PY - 2007/5/16

Y1 - 2007/5/16

N2 - In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.

AB - In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.

KW - Concentration

KW - Large deviation principle

KW - Minimizers

KW - Pinned wiener measure

KW - Scaling limit

UR - http://www.scopus.com/inward/record.url?scp=34249089863&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249089863&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34249089863

VL - 12

SP - 173

EP - 183

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

ER -