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The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals
Nualart, David Tudor, Ciprian A.
Nualart, David
Tudor, Ciprian A.
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Abstract
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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Date
2017
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Institute of Mathematical Statistics
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Keywords
Multiple stochastic integrals, Wiener chaos, Iterated Malliavin matrix, Covariance matrix, Absolute continuity
Citation
Nualart, D., & Tudor, C. A. (2017). The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals. The Annals of Probability, 45(1), 518-534.