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Register a new userStudy about stability of liner stochastic difference equations by using Lyapunov functions
دراسة حول استقرار المعادلات الفرقية العشوائية الخطية باستخدام دوال ليابونوف
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هدف هذا البحث هو بناء دالة ليابونوف لأحد المعادلات الفروقة العشوائية الخطية سنستخدم في ذلك الطريقة العامة لبناء دالة ليابونوف للمعادلات الفروقة العشوائية و سنتمكن من استنتاج شروط جديدة كافيه لتحقق الاستقرار المقارب الوسطي بالتربيع للحل الصفري لأحد المعادلات الفروقة العشوائية الخطية ذات المعاملات الثابتة ، مستخدمين بذلك بعض المبرهنات و التعاريف الاساسية للاستقرار المقارب بالتربيع للمعادلات الفروقة العشوائية الخطية .
In this paper , we will discuss the way of construction of lyapunov function for some of linear stochastic difference equations We will use the general method of constructions of lyapunov function for stochastic difference equations and we will obtain a sufficient conditions of asymptotic mean square stability of zero solution for one of linear stochastic difference equations with constant coefficient ,By using of some main theorems and definitions for asymptotic mean square stability for linear stochastic difference equations .
References used
CARABALLO, T., REAL, J. and SHAIKHET, L. 2007. Method of Lyapunov functionals construction in stability of delay evolution equations. Journal of mathematical analysis and applications, 334(2), pp.1130-1145
KOLMANOVSKII, V. and SHAIKHET, L. 2002 - Construction of Lyapunov Functionals for Stochastic Hereditary Systems: A Survey of Some Recent Results . Mathematical and Computer Modeling , v. 36 , pp. 691-716
KOLMANOVSKII, V. and SHAIKHET, L .1995 - General method of lyapunov functionals construction for stability investigation of stochastic difference equations .in Dynamical system and Applications , v.4, pp.397-439
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Stochastic matrix.
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Approximate stability in the quadratic middle.
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