Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes
P. W. Glynn and R. J. Wang
Submitted for publication.
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting disions 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 disions 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.