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

J. R. Baxter, N. C. Jain, S. R.S. Varadhan

Research output: Contribution to journalArticle

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 Lt(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 Lt(w, ˙) cannot hold with any rate function.

Original languageEnglish (US)
Pages (from-to)911-923
Number of pages13
JournalCommunications on Pure and Applied Mathematics
Volume44
Issue number8-9
DOIs
StatePublished - 1991

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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