Application of the general method of Lyapunov functionals construction for difference Volterra equations (Q1767834)

The paper is concerned with a stochastic difference equation in the form \[ x_{i+1}=\eta_{i+1} +F(i,x_0,\dots, x_i). \] The mean square integrability and asymptotical stability of the solution are studied by using the formal procedure of Lyapunov functionals. This procedure is demonstrated for a linear Volterra equation with constant coefficients. The region of mean square integrability is discussed for a special class of equations.