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