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The Breuer–Major theorem in total variation: Improved rates under minimal regularity.
- Source :
-
Stochastic Processes & Their Applications . Jan2021, Vol. 131, p1-20. 20p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RATES
*ESTIMATES
*DENSITY
*MATHEMATICAL equivalence
*DISTANCES
*GAUSSIAN processes
Subjects
Details
- Language :
- English
- ISSN :
- 03044149
- Volume :
- 131
- Database :
- Academic Search Index
- Journal :
- Stochastic Processes & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 147155296
- Full Text :
- https://doi.org/10.1016/j.spa.2020.08.007