Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes

TL;DR

This paper extends central limit theorems and large deviations principles to additive functionals of reflecting diffusions, including boundary reflection terms, with applications in queueing theory and economics.

Contribution

It develops new CLT and large deviations results for reflecting diffusions, incorporating boundary reflection effects, and derives PDEs for explicit computation of key quantities.

Findings

Established CLT and large deviations for reflecting diffusions with boundary terms

Derived PDEs for mean, variance, and rate functions

Applicable to queueing and economic models

Abstract

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary reflection that has occurred. Extending the known central limit and large deviations theory for Markov processes to include additive functionals that incorporate boundary reflection is important in many applications settings in which reflecting diffusions arise, including queueing theory and economics. In particular, the paper establishes the partial differential equations that must be solved in order to explicitly compute the mean and variance for the CLT, as well as the associated rate function for the large deviations principle.