The Annals of Probability
- Ann. Probab.
- Volume 45, Number 1 (2017), 518-534.
The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals
The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the determinant of its iterated Malliavin matrices. As an application, we show that the vector is not absolutely continuous if and only if its components are proportional.
Ann. Probab., Volume 45, Number 1 (2017), 518-534.
Received: February 2014
Revised: November 2014
First available in Project Euclid: 26 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G15: Gaussian processes
Nualart, David; Tudor, Ciprian A. The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals. Ann. Probab. 45 (2017), no. 1, 518--534. doi:10.1214/15-AOP1015. https://projecteuclid.org/euclid.aop/1485421338