Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 9, 12 pp.
Almost sure limit theorems on Wiener chaos: the non-central case
In , a framework to prove almost sure central limit theorems for sequences $(G_n)$ belonging to the Wiener space was developed, with a particular emphasis of the case where $G_n$ takes the form of a multiple Wiener-Itô integral with respect to a given isonormal Gaussian process. In the present paper, we complement the study initiated in , by considering the more general situation where the sequence $(G_n)$ may not need to converge to a Gaussian distribution. As an application, we prove that partial sums of Hermite polynomials of increments of fractional Brownian motion satisfy an almost sure limit theorem in the long-range dependence case, a problem left open in .
Electron. Commun. Probab., Volume 24 (2019), paper no. 9, 12 pp.
Received: 3 October 2018
Accepted: 18 January 2019
First available in Project Euclid: 15 February 2019
Permanent link to this document
Digital Object Identifier
Primary: 60F05: Central limit and other weak theorems 60G22: Fractional processes, including fractional Brownian motion 60G15: Gaussian processes 60H05: Stochastic integrals 60H07: Stochastic calculus of variations and the Malliavin calculus
Azmoodeh, Ehsan; Nourdin, Ivan. Almost sure limit theorems on Wiener chaos: the non-central case. Electron. Commun. Probab. 24 (2019), paper no. 9, 12 pp. doi:10.1214/19-ECP212. https://projecteuclid.org/euclid.ecp/1550199821