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)xµk
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 , µi > 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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