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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 15 open journal systems 


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.


Full text: PDF

Pages: 447-480

Published on: April 13, 2007
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Electronic Journal of Probability. ISSN: 1083-6489