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統計数学セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 担当者 | 吉田朋広、荻原哲平、小池祐太 |
|---|---|
| セミナーURL | http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ |
| 目的 | 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. |
2016年12月01日(木)
16:00-18:00 数理科学研究科棟(駒場) 052号室
Ciprian Tudor 氏 (Université Lille 1)
On the determinant of the Malliavin matrix and density of random vector on Wiener chaos
Ciprian Tudor 氏 (Université Lille 1)
On the determinant of the Malliavin matrix and density of random vector on Wiener chaos
[ 講演概要 ]
A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order, we prove that two random variables in the same Wiener chaos either admit a joint density, either are proportional and that the result is not true for random variables in Wiener chaoses of different orders.
A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order, we prove that two random variables in the same Wiener chaos either admit a joint density, either are proportional and that the result is not true for random variables in Wiener chaoses of different orders.
