Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations.

*(English)*Zbl 0883.39005Summary: Many processes in automatic regulation, physics, mechanics, biology, economy, ecology, etc. can be modelled by hereditary systems. One of the main problems for the theory of such systems and their applications is connected with stability. Many stability results were obtained by the construction of appropriate Lyapunov functionals. At present, a method is proposed which allows us, in some sense, to formalize the procedure of constructing the corresponding Lyapunov functionals. In this work, by virtue of the proposed procedure, necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations are obtained.

##### MSC:

39A11 | Stability of difference equations (MSC2000) |

##### Keywords:

hereditary systems; stability; Lyapunov functionals; stochastic linear difference equations
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\textit{L. Shaikhet}, Appl. Math. Lett. 10, No. 3, 111--115 (1997; Zbl 0883.39005)

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##### References:

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