Construction of Lyapunov functionals for stochastic difference equations with continuous time (Q1877719)

The author considers a stochastic difference equation with continuous time \[ x(t+h_0)=a_1\bigl(t,x(t),x(t-h_1),\dots\bigr)+ a_2\bigl(t,x(t), x(t-h_1),\dots \bigr)\xi(t+h_0),\;t<t_0-h_0, \] where the perturbations \(\xi(t)\) are stationary stochastic processes. Results on asymptotic mean square quasistability are obtained with the help of the Lyapunov functionals approach. An example of a linear difference equation with different stability regions is given.