الفهرس 
Chapter 1 : IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis, consisting of five chapters, the general method of Lyapunov functionals construction for stochastic difference problem is expounded. Taking into account that our general method of Lyapunov functionals construction has been applied for difference equations with constant coefficients and also with random coefficients under mean square and mean fourth calculus in stationary and non-stationary cases. Additionally, the summability study has been discussed in the last chapter.
Content of the thesis/ the dissertationis in (5) chapters as follow:
Chapter one:
This chapter is concerned with some definitions and remarks for probability theory, stochastic processes; mean square and mean fourth calculus. Additionally, some information according to the difference equations.
Chapter two:
presents basic definitions, Lyapunov type theorems, formal
procedure of Lyapunov functionals construction and some useful lemmas.
The procedure of Lyapunov functionals construction technique is applied in different ways for some case studies of a simple stochastic difference equation with constant and random coefficients for getting different asymptotic stability conditions asymptotic stability of the zero solution of this equation.
Chapter three:
Is concerned with the procedure of Lyapunov functionals construction different types
of sufficient stability conditions are obtained for linear equations with deterministic and random non-stationary coefficients.
Chapter four:
Is concerned with the procedure of Lyapunov functionals construction different types
of sufficient stability conditions are obtained for linear equations with deterministic and random stationary coefficients.
Chapter five:
Is concerned with the Stochastic Volterra difference equation of second-kind in two case studies and we will focus on the summablity in mean square and mean fourth sense of the stochastic process solutions using the Lyapunov functionals construction technique.