Moment bounds and central limit theorem for functions of Gaussian vectors

✍ Scribed by Philippe Soulier

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 136 KB
• Volume: 54
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00061-x

✦ Synopsis

In this note, bounds for moments of functions of Gaussian vectors are proved, generalizing earlier results by Taqqu (Z. Wahrscheinlichkeitstheorie verw. Gebite 40 (1977) 203) and Arcones (Ann. probab. 15 (4) (1994) 2243). These bounds are used to derive a Lindeberg-Levy central limit theorem for triangular arrays of functions of Gaussian vectors. Statistical applications for long range dependent processes are given.