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The influence of deterministic noise on empirical measures generated by stationary processes
Author(s):
Youri
Davydov;
Ricardas
Zitikis
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1203-1210.
MSC (2000):
Primary 60G10, 60B10;
Secondary 60G57
Posted:
June 23, 2003
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Abstract:
We consider weak convergence of empirical measures generated by stationary random process  perturbed by deterministic noise  . We assume that the noise  has asymptotic distribution. In particular, we demonstrate that if the process  is ergodic, or satisfies some mixing assumptions, then the influence of deterministic noise  on  is the same as it would be if  were stochastic. Such results are of importance when investigating fluctuations and convex rearrangements of stochastic processes.
References:
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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:
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
Posted:
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 of article:
Copyright
2003,
American Mathematical Society
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