Dichotomy in a scaling limit under wiener measure with density

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)173-183
Number of pages11
JournalElectronic Communications in Probability
Volume12
Publication statusPublished - 2007 May 16
Externally publishedYes

Fingerprint

Wiener Measure
Scaling Limit
Dichotomy
Minimizer
Large Deviation Principle
Law of large numbers
Large Deviations
Probability Measure
Asymptotic Behavior
Scaling
Distinct
Converge
Large deviations
Model
Asymptotic behavior

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.

In: Electronic Communications in Probability, Vol. 12, 16.05.2007, p. 173-183.

Research output: Contribution to journalArticle

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