2007/12/22 by Xavier Bardina, Maria Jolis, Bardina, Xavier +4
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.0712.3837
arxiv created 2007/12/22 · openalex publication_date 2007/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the convergence to the multiple Wiener-Itô 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 C0([0,T]). Using these processes, we construct a family that converges weakly, in the sense of the finite dimensional distributions, to the multiple Wiener-Itô integral process of a function f∈ L2([0,T]n). We prove also the weak convergence in the space \mathcal C0([0,T]) to the second order integral for two important families of processes that converge to a standard Brownian motion.