Higher order asymptotics for large deviations -- Part I
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth Expansions for the Central Limit Theorem. We apply our results to show that Diophantine iid sequences, finite state Markov chains, strongly ergodic Markov chains and Birkhoff sums of smooth expanding maps & subshifts of finite type satisfy these strong large deviation results.
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Phillip Griffiths Assistant Research Professor
I am a Griffiths Assistant Research Professor at the Department of Mathematics at Duke University. Prior to arriving at Duke, I completed my Ph.D. from the Department of Mathematics at the University of Maryland. The main focus of my research is asymptotic problems arising from Branching Processes, Branching Diffusions and related Dynamical Systems.