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Theory of Probability and Mathematical Statistics

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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 | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. M. F. Gorodnīĭ, Solutions of a stochastic difference equation that are stationary and bounded in the mean, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 8 (2002), 12–16 (Ukrainian, with English summary). MR 2009511
  • 2. S. Bochner and R. S. Phillips, Absolutely convergent Fourier expansions for non-commutative normed rings, Ann. of Math. (2) 43 (1942), 409–418. MR 0007939
  • 3. M. F. Gorodniĭ, Bounded and periodic solutions of a difference equation and its stochastic analogue in a Banach space, Ukrain. Mat. Zh. 43 (1991), no. 1, 41–46 (Russian, with Ukrainian summary); English transl., Ukrainian Math. J. 43 (1991), no. 1, 32–37. MR 1098269, 10.1007/BF01066900
  • 4. V. M. Kruglov, Dopolnitelnye glavy teorii veroyatnostei, “Vyssh. Shkola”, Moscow, 1984 (Russian). MR 756812
  • 5. L. V. Kantorovich and G. P. Akilov, Functional analysis, 2nd ed., Pergamon Press, Oxford-Elmsford, N.Y., 1982. Translated from the Russian by Howard L. Silcock. MR 664597
  • 6. A. Ya. Dorogovtsev, Stability of periodic solutions of operator equations with perturbation coefficients, Exploring stochastic laws, VSP, Utrecht, 1995, pp. 111–119. MR 1713997
  • 7. A. Ya. Dorogovtsev, Stability of bounded and stationary solutions of linear equations with respect to perturbations of operator coefficients, Dokl. Akad. Nauk 345 (1995), no. 4, 448–450 (Russian). MR 1376444

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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

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