Stable convergence of generalized L2 stochastic integrals and
the principle of conditioning
Peccati Giovanni, Université Paris VI
Murad S Taqqu, Boston University
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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