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2007 Dichotomy in a scaling limit under Wiener measure with density
Tadahisa Funaki
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Electron. Commun. Probab. 12: 173-183 (2007). DOI: 10.1214/ECP.v12-1271


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.


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Tadahisa Funaki. "Dichotomy in a scaling limit under Wiener measure with density." Electron. Commun. Probab. 12 173 - 183, 2007.


Accepted: 16 May 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1128.60021
MathSciNet: MR2318164
Digital Object Identifier: 10.1214/ECP.v12-1271

Primary: 60F10
Secondary: 82B24 , 82B31

Keywords: Concentration , large deviation principle , minimizers , pinned Wiener measure , Scaling limit


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