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Dichotomy in a scaling limit under Wiener measure with density
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Tadahisa Funaki, Graduate School of Mathematical Sciences, The University of Tokyo
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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.
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Full text: PDF
Pages: 173-183
Published on: May 16, 2007
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Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X |
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