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

Do Duc Thuan and Nguyen Hong Son

International Journal of Systems Science, 2022, vol. 53, issue 10, 2063-2074

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.

Date: 2022
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DOI: 10.1080/00207721.2022.2037781

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