We derive the chaotic expansion of the product of nthand ®rst-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integral...

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset L0 ⊂ L satisfying that, for any F∞ ∈ L0, the convergence of only a finite number of cumulants suffices to imply the convergence in law of any sequence in the second Wiener chaos to F∞. This result is in the spirit of the seminal paper [12], in which Nualart and Peccati discovered ...

We compute the Wiener-Poisson expansion of square-integrable functionals of a nite number of Poisson jump times in series of multiple Poisson stochastic integrals.

Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the “principle of conditioning”, to study their stable convergence towards mixtures of infinitely divisible distributions. Our results apply, in particular, to multiple integrals with respect to independently scattered and square ...