Dichotomy in a scaling limit underwiener measure with density

Tadahisa Funaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Publication statusPublished - 2007 Jan 1
Externally publishedYes


  • Concentration
  • Large deviation principle
  • Minimizers
  • Pinned Wiener measure
  • Scaling limit

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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