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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Estimates for the distribution of the supremum of square-Gaussian stochastic processes defined on 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