Four moments theorems on Markov chaos
S Bourguin, S Campese, N Leonenko, MS Taqqu - The Annals of Probability, 2019 - JSTOR
S Bourguin, S Campese, N Leonenko, MS Taqqu
The Annals of Probability, 2019•JSTORWe 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. These results are obtained by first
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, which is
of independent interest, and making use of the new concept of chaos grade. For the heavy …
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. These results are obtained by first
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, which is
of independent interest, and making use of the new concept of chaos grade. For the heavy …
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. These results are obtained by first 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, which is of independent interest, and making use of the new concept of chaos grade. For the heavy-tailed Pearson distributions, this seems to be the first time that sufficient conditions in terms of (finitely many) moments are given in order to converge to a distribution that is not characterized by its moments.
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