Spatializing random measures: Doubly indexed processes and the large deviation principle
Publication Date
1999
Journal or Book Title
ANNALS OF PROBABILITY
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.
Pages
297-324
Volume
27
Issue
1
Recommended Citation
Boucher, C; Ellis, RS; and Turkington, B, "Spatializing random measures: Doubly indexed processes and the large deviation principle" (1999). ANNALS OF PROBABILITY. 959.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/959
Comments
The published version is located at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aop/1022677264