Four moments theorems on Markov chains
Files
First author draft
Date
Authors
Bourguin, S.
Campese, Simon
Leonenko, Nikolai
Taqqu, Murad
Version
First author draft
OA Version
Citation
S. Bourguin, Simon Campese, Nikolai Leonenko, Murad Taqqu. "Four moments theorems on Markov chains." Annals of Probability, Volume 47, Number 3 (2019), 1417-1446. https://doi.org/10.1214/18-AOP1287
Abstract
We obtain quantitative Four Moments Theorems establishing convergence
of the laws of elements of a Markov chaos to a Pearson distribution,
where the only assumptionwemake on the Pearson distribution is that it admits
four moments. While in general one cannot use moments to establish convergence
to a heavy-tailed distributions, we provide a context in which only the
first four moments suffices. These results are obtained by proving a general
carré du champ bound on the distance between laws of random variables in the
domain of a Markov diffusion generator and invariant measures of diffusions.
For elements of a Markov chaos, this bound can be reduced to just the first four
moments.