The influence of deterministic noise on empirical measures generated by stationary processes
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- by Youri Davydov and Ričardas Zitikis
- Proc. Amer. Math. Soc. 132 (2004), 1203-1210
- DOI: https://doi.org/10.1090/S0002-9939-03-07156-9
- Published electronically: June 23, 2003
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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.References
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Bibliographic 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