The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals

• David Nualart ^[1] ; Ciprian A. Tudor ^[2]
  1. [1] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
  2. [2] Université de Lille
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 1, 2017, págs. 518-534
• Idioma: inglés
• DOI: 10.1214/15-AOP1015
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• Resumen

  • 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.