TY - JOUR

T1 - Dichotomy in a scaling limit underwiener measure with density

AU - Funaki, Tadahisa

PY - 2007/1/1

Y1 - 2007/1/1

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

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U2 - 10.1214/ECP.v12-1271

DO - 10.1214/ECP.v12-1271

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 -