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    Absolute continuity and convergence of densities for random vectors on Wiener chaos

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    Nualart_et_al_WienerChaos.pdf (457.6Kb)
    Issue Date
    2013-02-11
    Author
    Nourdin, Ivan
    Nualart, David
    Poly, Guillaume
    Publisher
    Institute of Mathematical Statistics (IMS)
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    The aim of this paper is to establish some new results on the absolute continuity and the convergence in total variation for a sequence of d-dimensional vectors whose components belong to a finite sum of Wiener chaoses. First we show that the probability that the determinant of the Malliavin matrix of such vectors vanishes is zero or one, and this probability equals to one is equivalent to say that the vector takes values in the set of zeros of a polynomial. We provide a bound for the degree of this annihilating polynomial improving a result by Kusuoka. On the other hand, we show that the convergence in law implies the convergence in total variation, extending to the multivariate case a recent result by Nourdin and Poly. This follows from an inequality relating the total variation distance with the Fortet-Mourier distance. Finally, applications to some particular cases are discussed.
    Description
    This is the publisher's version, also available electronically from http://ejp.ejpecp.org/article/view/2181
    URI
    http://hdl.handle.net/1808/14479
    DOI
    https://doi.org/10.1214/EJP.v18-2181
    ISSN
    1083-6489
    Collections
    • Distinguished Professors Scholarly Works [918]
    • Mathematics Scholarly Works [283]
    Citation
    Nourdin et al. (2013). Absolute continuity and convergence of densities for random vectors on Wiener chaos. Electronic Journal of Probability 18:41658.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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