TY - JOUR
T1 - On the convergence to the multiple Wiener-Itô integral
AU - Jolis, Maria
AU - Tudor, Ciprian A.
AU - Bardina, Xavier
PY - 2009/4/1
Y1 - 2009/4/1
N2 - 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.
AB - 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.
KW - Weak convergence
KW - Multiple Wiener-Itô integrals
KW - Donsker theorem
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=3074350
UR - https://www.scopus.com/pages/publications/62849095605
U2 - 10.1016/j.bulsci.2008.09.002
DO - 10.1016/j.bulsci.2008.09.002
M3 - Article
SN - 0007-4497
VL - 133
SP - 257
EP - 271
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
ER -