Large deviation properties of weakly interacting processes via weak convergence methods
Abstract
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay.
Cite
@article{arxiv.1009.6030,
title = {Large deviation properties of weakly interacting processes via weak convergence methods},
author = {Amarjit Budhiraja and Paul Dupuis and Markus Fischer},
journal= {arXiv preprint arXiv:1009.6030},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP616 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)