## The Annals of Probability

### On Some Applicable Versions of Abstract Large Deviations Theorems

Dimitry Ioffe

#### Abstract

Two algorithms for calculating rate functions for a family of measures $\{\mu_\varepsilon\}$ on a $B$-space $X$ are considered. The first one is a relaxed version of the Fenchel transform type theorem for convex rate functions. The second gives conditions under which $\{\mu_\varepsilon\}$ can be replaced by a more convenient family $\{\mu^x_\varepsilon\}$ near admissible points $x \in X$ such that rate functions for both families coincide near $x$. As an example, we apply both techniques to investigate large deviation properties of some reaction-diffusion equations with quick random noise.

#### Article information

Source
Ann. Probab. Volume 19, Number 4 (1991), 1629-1639.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176990226

Digital Object Identifier
doi:10.1214/aop/1176990226

Mathematical Reviews number (MathSciNet)
MR1127718

Zentralblatt MATH identifier
0754.60027

JSTOR