Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

Authors:	Ciprian A Tudor Nakahiro Yoshida

Affiliation:	1. Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq, France;2. Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153, Japan;3. Japan Science and Technology Agency, CREST, Japan;4. ISMMA, Romanian Academy, Bucharest, Romania

Abstract:	We develop the asymptotic expansion theory for vector-valued sequences ${(F_{N})}_{N \geq 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_{N}$ . Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_{N}$ and we illustrate our results by several examples.

Keywords:	Corresponding author 62M09 60F05 62H12 Asymptotic expansion Stein–Malliavin calculus Quadratic variation Fractional Brownian motion Central limit theorem Fourth moment theorem
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