We show that the general stable convergence results proved in Peccati and Taqqu (2007) for generalized adapted stochastic integrals can be used to obtain limit theorems for multiple stochastic integrals with respect to independently scattered random measures. Several applications are developed in a companion paper (see Peccati and Taqqu, 2008a), where we prove central limit results involving si...

Stochastic integration rules are derived for infinite integration intervals, generalizing rules developed by Siegel and O’Brien [SIAM J. Sci. Statist. Comput., 6 (1985), pp. 169–181] for finite intervals. Then random orthogonal transformations of rules for integrals over the surface of the unit m-sphere are used to produce stochastic rules for these integrals. The two types of rules are combine...

In [10] a “direct” stochastic transfer principle was introduced, which represented multiple integrals with respect to fractional Brownian motion in terms of multiple integrals with respect to standard Brownian motion. The method employed in [10] involved an operator Γ (n) H , mapping a class of functions LH to L 2. However, the operator does not map LH onto L 2. Hence Γ (n) H is not invertible....

Stochastic diierential equations in R n with random coeecients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W 2 for some > 1=2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution proced...