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2019 Almost sure limit theorems on Wiener chaos: the non-central case
Ehsan Azmoodeh, Ivan Nourdin
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP212


In [1], 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 [1], 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 [1].


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Ehsan Azmoodeh. Ivan Nourdin. "Almost sure limit theorems on Wiener chaos: the non-central case." Electron. Commun. Probab. 24 1 - 12, 2019.


Received: 3 October 2018; Accepted: 18 January 2019; Published: 2019
First available in Project Euclid: 15 February 2019

zbMATH: 1412.60041
MathSciNet: MR3916341
Digital Object Identifier: 10.1214/19-ECP212

Primary: 60F05, 60G15, 60G22, 60H05, 60H07


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