Rodkina, Alexandra E.
Author Affiliation, Ana.
Department of Mathematics and Computer Science
On asymptotic stability of nonlinear stochastic systems with delay
Cubo: A mathematical journal
Date of Publication
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.....