Stability estimates for linear stochastic systems with deviating argument of neutral type (Q1336006)

The system of stochastic differential equations \[ d \bigl[ x(t) - Dx(t- \tau) \bigr] = \bigl[ A_ 0 x(t) + A_ 1 x(t - \tau) \bigr] dt + \bigl[ B_ 0 x(t) + B_ 1 x(t - \tau) \bigr] d \omega_ t, \] where \(D, A_ 0, A_ 1, B_ 0, B_ 1\) are square matrices with constant coefficients, \(\omega (t)\) is a scalar standard Wiener process and \(\tau > 0\) is a constant lag, is considered. Sufficient conditions for the stability of this system are established by using the method of stochastic Lyapunov functions.