Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike

2016/12/01

16:00-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Ciprian Tudor (Université Lille 1)
On the determinant of the Malliavin matrix and density of random vector on Wiener chaos

[ Abstract ]
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.