Some familiar examples for which the large deviation principle does not hold | Zendy

Baxter J. R. | Zendy; Jain N. C. | Zendy; Varadhan S. R. S. | Zendy

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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

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.

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