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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The influence of deterministic noise on empirical measures generated by stationary processes
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by Youri Davydov and Ričardas Zitikis PDF
Proc. Amer. Math. Soc. 132 (2004), 1203-1210 Request permission

Abstract:

We consider weak convergence of empirical measures generated by stationary random process $X$ perturbed by deterministic noise $N$. We assume that the noise $N$ has asymptotic distribution. In particular, we demonstrate that if the process $X$ is ergodic, or satisfies some mixing assumptions, then the influence of deterministic noise $N$ on $X$ is the same as it would be if $N$ were stochastic. Such results are of importance when investigating fluctuations and convex rearrangements of stochastic processes.
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Additional Information
  • Youri Davydov
  • Affiliation: Laboratoire de Mathématiques Appliquées, Université des Sciences et Technologies de Lille, CNRS-FRE 2222, 59655 Villeneuve d’Ascq Cedex, France
  • Email: Youri.Davydov@univ-lille1.fr
  • Ričardas Zitikis
  • Affiliation: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada N6A 5B7
  • Email: zitikis@stats.uwo.ca
  • Received by editor(s): February 4, 2002
  • Received by editor(s) in revised form: December 17, 2002
  • Published electronically: June 23, 2003
  • Additional Notes: The first author was supported in part by the RFBR Grant 99-01-00112.
    The second author was supported in part by an NSERC of Canada individual research grant at the University of Western Ontario.
  • Communicated by: Claudia M. Neuhauser
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1203-1210
  • MSC (2000): Primary 60G10, 60B10; Secondary 60G57
  • DOI: https://doi.org/10.1090/S0002-9939-03-07156-9
  • MathSciNet review: 2045439