2011
DOI: 10.1016/j.spa.2010.12.006
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Quantitative Breuer–Major theorems

Abstract: This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their pe… Show more

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Cited by 54 publications
(78 citation statements)
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“…For the proof of quantitative Breuer-Major theorems in [8], the upper bound of the Kolmogorov distance is obtained by using the relation (see…”
Section: Introductionmentioning
confidence: 99%
“…For the proof of quantitative Breuer-Major theorems in [8], the upper bound of the Kolmogorov distance is obtained by using the relation (see…”
Section: Introductionmentioning
confidence: 99%
“…Nevertheless, following the approach developed in Nourdin, Peccati and Podolskij [5] (see also [4,Chapter 7]) we prove the following result. Theorem 1.1.…”
Section: Introductionmentioning
confidence: 58%
“…The second condition in (1.4) ensures that f i can be expanded in Hermite polynomials, namely 5) whereas from the first one we deduce that a i,0 = 0. The first goal of the present paper is to answer the following question.…”
Section: Introductionmentioning
confidence: 99%
“…Here again, one can use results of [24] to get explicit estimates on the speed of convergence for this CLT.…”
Section: Remarkmentioning
confidence: 99%