Remote Access 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
Full-text PDF

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,
  • 4. V. M. Kruglov, \cyr Dopolnitel′nye glavy teorii veroyatnosteĭ, “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

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G10, 39A10, 47A50

Retrieve articles in all journals with MSC (2000): 60G10, 39A10, 47A50

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

American Mathematical Society