Bourguin, S.Campese, SimonLeonenko, NikolaiTaqqu, Murad2020-01-172020-01-17S. 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-AOP12870091-1798https://hdl.handle.net/2144/39118We 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.en-USMarkov operatorDiffusion generatorGamma calculusPearson distributionsStein's methodLimit theoremsStatistics & probabilityStatisticsFour moments theorems on Markov chainsArticledoi:10.1214/18-AOP12870000-0002-1145-9082 (Taqqu, Murad)312757