IJPAM: Volume 74, No. 2 (2012)
DELAY DIFFERENTIAL EQUATIONS BY NOISE
Johnson Adekunle Osilagun, Suraju Olusegun Ajadi
Department of Mathematics
Obafemi Awolowo University
Department of Mathematical Sciences
Olabisi Onabanjo University
Abstract. This paper is concerned with the stabilisation of finite dimensional stochastic delay differential equation of the form
where , , . Under more general conditions, we show that a linear multiplicative noise can always stabilise a general finite-dimensional functional differential equation whenever the delay is sufficiently small. Our results complement and improve existing results, and are also in line with the results of Appleby  which in itself generalised some well known results in the literature.
Received: June 16, 2011
AMS Subject Classification: 39A11, 60F15, 65C30, 34D40, 34D45
Key Words and Phrases: stochastic delay differential equations, Ito's theorem, stability, noise
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395