We consider the system of stochastic differential equations with delay and with non-autonomous nonlinear main part
Here h ≥ 0, [X]tt - h (s) = X(s), when s ⋲ [t - h, t], t > h, [X]tt - h (s) = 𝜙(s), when s ⋲ [-∞, 0], 𝜙(s) is a given initial process, X= (x1, x2,..., xn)T, ui > 1 are rational numbers with odd numerators and denominators, wt is a Wiener process. For different types of delays in coefficients fi (t, [X]tt - h) and 𝜎i (t, [X]tt - h) we prove almost sure asymptotic stability of a trivial solution to the system (1) when 𝜙(s) ≡ 0.
@article{1617,
title = {On Asymptotic Stability of Nonlinear Stochastic Systems with Delay},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1617}
}
Rodkina, A. On Asymptotic Stability of Nonlinear Stochastic Systems with Delay. CUBO, A Mathematical Journal, Tome 7 (2005) 20 p. http://gdmltest.u-ga.fr/item/1617/