## 統計数学セミナー

担当者 吉田朋広、荻原哲平、小池祐太 http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

### 2018年10月30日(火)

15:30-16:40   数理科学研究科棟(駒場) 126号室
Ciprian A. Tudor 氏 (Université de Lille 1, Université de Panthéon-Sorbonne Paris 1)
Asymptotic expansion for random vectors
[ 講演概要 ]
We develop the asymptotic expansion theory for vector-valued sequences $F_{N}$ of random variables. We find the second-order term in the expansion of the density of $F_{N}$, based on assumptions in terms of the convergence of the Stein-Malliavin matrix associated to the sequence $F_{N}$ . Our approach combines the classical Fourier approach and the recent theory on Stein method and Malliavin calculus. We find the second order term of the asymptotic expansion of the density of $F_{N}$ and we discuss the main ideas on higher order asymptotic expansion. We illustrate our results by several examples.