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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Berkolaiko, G; Rodkina, Alexandra
Author Affiliation, Ana.
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Article Title
Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equation
Medium Designator
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Connective Phrase
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Journal Title
Difference Equations and Applications
Translated Title
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Reprint Status
Refereed
Date of Publication
2006
Volume ID
12
Issue ID
6
Page(s)
535-553
Language
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Connective Phrase
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Location/URL
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ISSN
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Notes
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Abstract
We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial value X_0, non-random decaying free coefficient S_n and independent random variables \xi_n. We establish results on \as convergence of solutions X_n to zero. The necessary conditions we find tie together certain moments of the noise \xi_n and the rate of decay of S_n. To ascertain sharpness of our conditions we discuss some situations when X_n diverges. We also establish a result concerning the rate of decay of X_n to zero.....
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