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Zbl 0883.39005
Shaikhet, L.
Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations. (English)
[J] Appl. Math. Lett. 10, No.3, 111-115 (1997). ISSN 0893-9659

Summary: 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 2000:: *39A11 Stability of difference equations

Keywords: hereditary systems; stability; Lyapunov functionals; stochastic linear difference equations

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Zentralblatt MATH Berlin [Germany]