On the convergence to the multiple Wiener-Itô integral

Xavier Bardina, Maria Jolis, Ciprian A. Tudor

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

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 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 C0 ([0, T]) to the second-order integral for two important families of processes that converge to a standard Brownian motion. © 2008 Elsevier Masson SAS. All rights reserved.
Original languageEnglish
Pages (from-to)257-271
JournalBulletin des Sciences Mathematiques
Volume133
DOIs
Publication statusPublished - 1 Apr 2009

Keywords

  • Donsker theorem
  • Multiple Wiener-Itô integrals
  • Weak convergence

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