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

 

Wide sense stationary solutions of difference equations in a Banach space


Author: M. F. Gorodnii
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 29-35
MSC (2000): Primary 60G10, 39A10; Secondary 47A50
Published electronically: June 25, 2007
MathSciNet review: 2336776
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Abstract: A criterion is proved for the existence of a unique wide sense stationary solution of a linear difference equation with operator coefficients in a Banach space. The stability of this solution with respect to small perturbations of operator coefficients is proved.


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Additional Information

M. F. Gorodnii
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Glushkov Avenue, 6, Kyiv, 03127, Ukraine
Email: gorodnii@yandex.ru

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00695-3
PII: S 0094-9000(07)00695-3
Keywords: Difference equation, operator coefficients, wide sense stationary solutions
Received by editor(s): March 18, 2005
Published electronically: June 25, 2007
Article copyright: © Copyright 2007 American Mathematical Society