Article

Spatializing random measures: Doubly indexed processes and the large deviation principle

ANNALS OF PROBABILITY
Publication Date

1999
Abstract

The main theorem is the large deviation principle for the doubly indexed sequence of random measures Abstract
Here $\theta$ is a probability measure on a Polish space $\mathscr{X},{D_{r,k}k=1,\ldots,2^r}$ is a dyadic partition of $\mathscr{X}$ (hence the use of $2^r$ summands) satisfying $\theta{D_{r,k}}= 1/2^r$ and $L_{q,1}L_{q,2},\ldotsL_{q,2_r}$ is an independent, identically distributed sequesnce of random probability measures on a Ploish space$ \mathscr{Y}$ such that ${L_{q,k}q\in \mathsbb{N}}$ satisfies the large deviation principle with a convex rate function. A number of related asymptotic results are also derived.
The random measures $W_{ r,q}$ have important applications to the statistical mechanics of turbulence. In a companion paper, the large deviation principle presented here is used to give a rigorous derivation of maximum entropy principles arising in the well-known Miller–Robert theory of two-dimensional turbulence as well as in a modification of that theory recently proposed by Turkington.
Disciplines

Pages

297-324
Citation Information

C Boucher, RS Ellis and B Turkington. "Spatializing random measures: Doubly indexed processes and the large deviation principle" *ANNALS OF PROBABILITY*Vol. 27 Iss. 1 (1999)

Available at: http://works.bepress.com/richard_ellis/10/

The published version is located at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aop/1022677264