On some approach to investigation of a system of difference equations with random coefficients (Q2761548)

Let us consider the system of linear difference equations \(X_{n+1}=X_{n}+\mu A(n,\xi_{n})X_{n}\), where \(A(n,\xi_{n})\) is a matrix depending on a random process \(\xi_{n}\) and \(\mu\) is a small parameter. The author proposes an algorithm for constructing a system of difference equations for the mathematical expectation of \(X_{n}\). For the linear difference equation \(x_{n+1}=x_{n}+\mu a(\xi_{n})x_{n}\), where the random process \(\xi_{n}\) has three values, sufficient conditions of stability in the mean of the zero solution are obtained.