Journal
ANNALS OF PROBABILITY
Volume 45, Issue 1, Pages 518-534Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/15-AOP1015
Keywords
Multiple stochastic integrals; Wiener chaos; iterated Malliavin matrix; covariance matrix; absolute continuity
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Funding
- NSF [DMS-12-08625]
- CNCS (Romania) [PN-II-ID-PCCE-2011-2-0015]
- ARC [DP130102408]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1208625] Funding Source: National Science Foundation
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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.
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