Four moments theorems on Markov chains
MetadataShow full item record
First author draft
Citation (published version)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
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.