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 language||English (US)|
|Number of pages||13|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - 1991|
ASJC Scopus subject areas
- Applied Mathematics