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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Asymptotic stability of the maximum of normal stochastic processes


Author: I. K. Matsak
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 101-106
MSC (2000): Primary 60B12
Published electronically: December 30, 2009
MathSciNet review: 2494539
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Abstract: Under quite general conditions, we prove that the maximum of a sequence of normal stochastic processes in the space $ C_{[0,1]}$ is asymptotically stable almost surely.


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Additional Information

I. K. Matsak
Affiliation: Department of Operation Research, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: mik@unicyb.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00784-4
PII: S 0094-9000(09)00784-4
Keywords: Asymptotic stability, extremal values, normal stochastic processes, the space $C_{[0,1]}$
Received by editor(s): January 30, 2007
Published electronically: December 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society