Higher order asymptotics for large deviations -- Part I
Probability
2020-03-10 v4 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1811.06793,
title = {Higher order asymptotics for large deviations -- Part I},
author = {Kasun Fernando and Pratima Hebbar},
journal= {arXiv preprint arXiv:1811.06793},
year = {2020}
}
Comments
37 pages, 1 figure, original version split into two parts: discrete time (part I) and continuous time (Part II)