Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes
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.
KeywordsCentral Limit Theorem Additive Functional Large Deviation Principle Stochastic Calculus Boundary Reflection
The first author gratefully acknowledges the mentorship and friendship of Professor Miklós Csörgő, over the years, and Professor Csörgő’s influence on both his research direction and academic career in the years that have passed since his graduation as a student at Carleton University.
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