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Some familiar examples for which the large deviation principle does not hold
Author(s) -
Baxter J. R.,
Jain N. C.,
Varadhan S. R. S.
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440806
Subject(s) - rate function , mathematics , large deviations theory , brownian motion , function (biology) , regularization (linguistics) , mathematical analysis , statistical physics , pure mathematics , statistics , physics , computer science , evolutionary biology , artificial intelligence , biology
Abstract For a class of Markov processes (in continuous or discrete time) we show that if the full large deviation holds for normalized occupation time measures L t ( w , ˙) with some rate function J , then the lower semicontinuous regularization of J must agree with the rate function I introduced by M. D. Donsker and S. R. S. Varadhan. As a consequence we show that for processes such as Brownian motion the full large deviation principle for L t ( w , ˙) cannot hold with any rate function.