Solvability and stability of stochastic singular difference equations with constant coefficient matrices of index-ν

Abstract

In this paper, we shall deal with stochastic singular difference equations (SSDEs) with constant coefficient matrices and nonlinear stochastic perturbations. The solvability and stability of SSDEs are difficult to study because of the singularity of the leading coefficient matrix. An index-ν concept is derived and formulas of solution are established for these equations. The continuous dependence of solution on initial condition is also considered. Finally, the stability of SSDEs is studied by using the method of Lyapunov functions. Some examples are given to illustrate the results.