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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The influence of deterministic noise on empirical measures generated by stationary processes


Authors: Youri Davydov and Ricardas Zitikis
Journal: Proc. Amer. Math. Soc. 132 (2004), 1203-1210
MSC (2000): Primary 60G10, 60B10; Secondary 60G57
Published electronically: June 23, 2003
MathSciNet review: 2045439
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Abstract | References | Similar Articles | Additional Information

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

Ricardas Zitikis
Affiliation: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada N6A 5B7
Email: zitikis@stats.uwo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07156-9
PII: S 0002-9939(03)07156-9
Keywords: Stationary process, ergodic process, mixing process, empirical measure, weak convergence, strong convergence.
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
Article copyright: © Copyright 2003 American Mathematical Society