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Theory of Probability and Mathematical Statistics

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Estimates for the distribution of the supremum of square-Gaussian stochastic processes defined on noncompact sets


Authors: Yu. V. Kozachenko and T. V. Fedoryanich
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 81-97
MSC (2000): Primary 60G17; Secondary 60G07
DOI: https://doi.org/10.1090/S0094-9000-07-00683-7
Published electronically: January 17, 2007
MathSciNet review: 2213843
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Abstract: Estimates for the distribution of the supremum of square-Gaussian stochastic processes defined on $ \mathbb{R}^+$ are found in the paper. Using these results, we find estimates for the deviation in the uniform metric between the correlogram and the correlation function of a real stationary Gaussian stochastic process. A criterion for testing a hypothesis concerning the correlation function is also constructed.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kiev 03127, Ukraine
Email: yvk@univ.kiev.ua

T. V. Fedoryanich
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kiev 03127, Ukraine
Email: fedoryanich@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-07-00683-7
Keywords: Square-Gaussian processes, correlograms, stationary processes, a criterion for testing a hypothesis
Received by editor(s): November 15, 2004
Published electronically: January 17, 2007
Additional Notes: The first author was supported in part by the NATO Grant PST.CLG. 980408
Article copyright: © Copyright 2007 American Mathematical Society