### 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.

Original language | English (US) |
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Pages (from-to) | 911-923 |

Number of pages | 13 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 44 |

Issue number | 8-9 |

DOIs | |

State | Published - 1991 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Baxter, J. R., Jain, N. C., & Varadhan, S. R. S. (1991). Some familiar examples for which the large deviation principle does not hold.

*Communications on Pure and Applied Mathematics*,*44*(8-9), 911-923. https://doi.org/10.1002/cpa.3160440806