Events for 12/15/2021 from all calendars

Colloquium - Yeor Hafouta

Time: 4:00PM - 5:00PM

Location: ZOOM only

Speaker: Yeor Hafouta, The Ohio State University

Description:
Title: Optimal CLT rates and CLT expansions for inhomogeneous Markov chains.
Abstract: The classical Dobrushin's Central Limit Theorem yields the CLT for additive functionals of sufficiently well contracting inhomogeneous Markov chains. On the other hand, the classical Berry-Esseen theorem provides optimal convergence rates in the CLT for independent random variables. This is a quantified version of the CLT, and we will also discuss classical applications in statistics. By now optimal rates were obtained for homogeneous and sufficiently well contracting Markov chains. The first new result we will describe is a Berry-Esseen theorem (optimal CLT rates) for inhomogeneous uniformly elliptic Markov chains, whose main novelty is that we assume no growth rates on the variance of the underlying partial sums. I will also discuss optimal rates for sequential and random dynamical systems (everything will be defined in the talk). Another classical result for independent random variables are the so-called Edgeworth expansions, which provide a more accurate estimate than the Berry-Esseen theorem, with finer correction terms. Such results were obtained for homogeneous Markov chains, and for inhomogeneous Markov chains we obtain optimal conditions for Edgeworth expansions of an arbitrary order to hold, and without growth rates on the variances. If time permits we will also discuss the "canonical form" of the Edgeworth polynomials (correction terms).