On the convergence to the multiple Wiener-Ito integral

Details On the convergence to the multiple Wiener-Ito integral On the convergence to the multiple Wiener-Ito integral

2007-12-22

arxiv.org/abs/0712.3837v1

Mathematics

Probability

Scientific paper

We study the convergence to the multiple Wiener-It\^{o} integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin space, that converges weakly to a standard Brownian motion in $\mathcal C_0([0,T])$. Using these processes, we construct a family that converges weakly, in the sense of the finite dimensional distributions, to the multiple Wiener-It\^{o} integral process of a function $f\in L^2([0,T]^n)$. We prove also the weak convergence in the space $\mathcal C_0([0,T])$ to the second order integral for two important families of processes that converge to a standard Brownian motion.

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