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    Stable convergence of generalized L-2 stochastic integrals and the principle of conditioning

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    Date Issued
    2007-04-13
    Publisher Version
    10.1214/EJP.v12-404
    Author(s)
    Peccati, Giovanni
    Taqqu, Murad S.
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    Permanent Link
    https://hdl.handle.net/2144/37416
    Version
    First author draft
    Citation (published version)
    Giovanni Peccati, Murad S Taqqu. 2007. "Stable convergence of generalized L-2 stochastic integrals and the principle of conditioning." ELECTRONIC JOURNAL OF PROBABILITY, Volume 12, pp. 447 - 480 (34). https://doi.org/10.1214/EJP.v12-404
    Abstract
    We consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments, and use a decoupling technique, formulated as a «principle of conditioning», to study their stable convergence towards mixtures of infinitely divisible distributions. The goal of this paper is to develop the theory. Our results apply, in particular, to Skorohod integrals on abstract Wiener spaces, and to multiple integrals with respect to independently scattered and finite variance random measures. The first application is discussed in some detail in the final sectionof the present work, and further extended in a companion paper (Peccati and Taqqu (2006b)). Applications to the stable convergence (in particular, central limit theorems) of multiple Wiener-Itô integrals with respect to independently scattered (and not necessarily Gaussian) random measures are developed in Peccati and Taqqu (2006a, 2007). The present work concludes with an example involving quadratic Brownian functionals.
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