2013/07/05 by Peter W. Glynn, Glynn, Peter W., Rob J. Wang +1
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1307.1574
arxiv created 2014/07/08 · arxiv updated 2014/07/10
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.