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Theory of Probability and Mathematical Statistics

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Multidimensional weakly stationary random functions on semigroups


Authors: O. I. Ponomarenko and Yu. D. Perun
Translated by: V. V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 151-162
MSC (2000): Primary 60G10, 60G57, 60G15
Published electronically: January 17, 2007
MathSciNet review: 2213849
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider some problems in the spectral analysis of weakly stationary Hilbert-valued random functions on involutive semigroups. We obtain spectral representations for such functions and for their correlation functions. These representations are extensions and improvements of the corresponding results proved earlier by the first author and by V. Girardin and R. Senoussi.


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Additional Information

O. I. Ponomarenko
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: probab@univ.kiev.ua

Yu. D. Perun
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: perun@bank.gov.ua

DOI: https://doi.org/10.1090/S0094-9000-07-00689-8
Keywords: Random functions, spectral representations, involutive semigroup, weakly stationary random functions
Received by editor(s): December 3, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society