Abstract. Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriateâ€¦ (More)

Stability investigation of hereditary systems is connected often with construction of Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed in [1-9]â€¦ (More)

We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation dx(t)= (Î±x(t) +Î² âˆ« t 0 x(s)ds)dt + Ïƒx(tâˆ’â€¦ (More)

Some new Lyapunov-type theorems for stochastic differential equations of neutral type are proved. It is shown that these theorems simplify an application of Kolmanovskii and Shaikhet's general methodâ€¦ (More)

A nonlinear integro-differ ential equation of convolution type with order of nonlinearity more than one and a stable trivial solution is considered. The integral in this equation has an exponentialâ€¦ (More)

We investigate the long term behavior of solutions to a stochastic Volterra integro-differential equation with a fading memory; the fading memory is represented by using a decaying exponentialâ€¦ (More)

One general method of Lyapunov functionals construction which was used earlier both for stochastic differential equations with aftereffect and for stochastic difference equations with discrete timeâ€¦ (More)