About stability of nonlinear stochastic difference equations.

*(English)*Zbl 0959.60056Summary: Using the method of Lyapunov functionals construction, it is shown that investigation of stability in probability of nonlinear stochastic difference equation with order of nonlinearity more than one can be reduced to the investigation of asymptotic mean square stability of the linear part of this equation.

##### MSC:

60H25 | Random operators and equations (aspects of stochastic analysis) |

39A10 | Additive difference equations |

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\textit{B. Paternoster} and \textit{L. Shaikhet}, Appl. Math. Lett. 13, No. 5, 27--32 (2000; Zbl 0959.60056)

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##### References:

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