Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Almost sure convergence on chaoses


Authors: Guillaume Poly and Guangqu Zheng
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 60F99; Secondary 60H05
DOI: https://doi.org/10.1090/proc/14557
Published electronically: May 1, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on a fixed finite sum of chaoses forces the almost sure convergence of each chaotic component. Our strategy uses ``extra randomness'' and a simple conditioning argument. These ideas are close to the spirit of Stein's method of exchangeable pairs. Some natural questions are left open in this note.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 60F99, 60H05

Retrieve articles in all journals with MSC (2010): 60F99, 60H05


Additional Information

Guillaume Poly
Affiliation: Institut de recherche mathématique de Rennes (UMR CNRS 6625), Université de Rennes 1, Bâtiment 22–23, 263, avenue du Général Leclerc, 35042 Rennes Cedex, France
Email: guillaume.poly@univ-rennes1.fr

Guangqu Zheng
Affiliation: Department of Mathematics, University of Kansas, Snow Hall, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045-7594
Email: gzheng90@ku.edu

DOI: https://doi.org/10.1090/proc/14557
Keywords: Exchangeable pairs, Ornstein-Uhlenbeck semigroup, Wiener chaos, homogeneous sums.
Received by editor(s): October 2, 2018
Received by editor(s) in revised form: December 13, 2018
Published electronically: May 1, 2019
Communicated by: Zhen-Qing Chen
Article copyright: © Copyright 2019 American Mathematical Society