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Multidimensional weakly stationary random functions on semigroups
Author(s):
O.
I.
Ponomarenko;
Yu.
D.
Perun
Translated by:
V. V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 73
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 73
(2006),
151-162.
MSC (2000):
Primary 60G10, 60G57, 60G15
Posted:
January 17, 2007
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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.
References:
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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:
10.1090/S0094-9000-07-00689-8
PII:
S 0094-9000(07)00689-8
Keywords:
Random functions,
spectral representations,
involutive semigroup,
weakly stationary random functions
Received by editor(s):
3/DEC/2004
Posted:
January 17, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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