Four moments theorems on Markov chaos

2018/02/16 by Bourguin, Solesne, Campese, Simon, Leonenko, Nikolai +1 · 1 citation
#60F05 #60J35 #60J99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.06092

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 assumption we make 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.

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