The Breuer–Major theorem in total variation: Improved rates under minimal regularity

Ivan Nourdin, David Nualart and Giovanni Peccati

Stochastic Processes and their Applications, 2021, vol. 131, issue C, 1-20

Abstract: In this paper we prove an estimate for the total variation distance, in the framework of the Breuer–Major theorem, using the Malliavin–Stein method, assuming the underlying function g to be once weakly differentiable with g and g′ having finite moments of order four with respect to the standard Gaussian density. This result is proved by a combination of Gebelein’s inequality and some novel estimates involving Malliavin operators.

Keywords: Breuer–Major theorem; Integration by Parts; Rate of Convergence; Malliavin–Stein approach (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:131:y:2021:i:c:p:1-20

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DOI: 10.1016/j.spa.2020.08.007

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