Title :

The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals

Author(s) :

Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

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 ...
Show more >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 and this order is at most 4, 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.Show less >

Language :

Anglais

Comment :

Shortly after the publication of the first version of the paper on arxiv, we realized that the there is a mistake in one of the proofs. The formula for the determinant of the Malliavin matrix was correct but the relations (19) and (20) in the first version were wrong (or not yet proven).

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T10:18:13Z