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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Rodkina, Alexandra E.
Author Affiliation, Ana.
Department of Mathematics and Computer Science
Article Title
On asymptotic stability of nonlinear stochastic systems with delay
Medium Designator
n/a
Connective Phrase
n/a
Journal Title
Cubo: A mathematical journal
Translated Title
n/a
Reprint Status
n/a
Date of Publication
2005
Volume ID
07
Issue ID
N1
Page(s)
23-42
Language
n/a
Connective Phrase
n/a
Location/URL
n/a
ISSN
n/a
Notes
n/a
Abstract
We consider the system of stochastic differential equations with delay and with nonautonomous nonlinear main part dxi(t) = n Xk=1 pki(t)xk k (t) + fi t, [X]t-h t dt + i t, [X]t-h t dwt, i = 1, . . . , n, X(s) = (s), s 0. (1) Here h 0, [X]t-h t (s) = X(s), when s 2 [t - h, t], t > h, [X]t-h t (s) = (s), when s 2 [-1, 0], (s) is a given initial process, X = (x1, x2, . . . , xn)T , i > 1 are rational numbers with odd numerators and denominators, wt is a Wiener process. For different types of delays in coefficients fi t, [X]t-h t and i t, [X]t-h t we prove almost sure asymptotic stability of a trivial solution to the system (1) when (s) 0.....
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