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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Rodkina, Alexandra E.; Mao, Xuerong
Author Affiliation, Ana.
Department of Mathematics and Compuiter Science
Article Title
On boundedness and stability of solutions of nonlinear difference equation with nonmartingale type noise
Medium Designator
n/a
Connective Phrase
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Journal Title
Journal of Difference Equations and Applications
Translated Title
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Reprint Status
Refereed
Date of Publication
2001
Volume ID
7
Issue ID
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Page(s)
529-50
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
Consider a stochastic difference equation xi+1 = Gi [xi, xi-1, ...,xo] + fi[xi, xi-1,..., xo]+ k0 åsi-k[xi-k, xi-k-1,...,xo]xi+1-k, k=0 with the volterra type nonlinear main term G and Volterra type noise f+ åsi-k xi+1-k. Functions G, f, s supposed to be random, xi is a martingale-difference. In general, ko³ 1 so Eq. (1) cannot be considered as a stochastic equation with respect to the discrete semimartingale because the term åsi-k xi+1-k is not a martingale-difference. The main aim of this paper is to establish the sufficient conditions on the almost sure boundedness, asymptotic and exponential stability of the solutions. Equation (1) can be interpreted as a generalization of the equation describing the gain incurred by the insurance company in a year i+1. we therefore explore the possible application of our theory in this area.....
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