Lyapunov Functionals and Stability of Stochastic Difference Equations offers a comprehensive examination of the stability of stochastic difference equations, which are applicable in various scientific disciplines. The book discusses the construction of Lyapunov functionals to analyze the stability of both discrete and continuous stochastic Volterra difference equations. It begins with fundamental definitions and mathematical foundations and progresses to general stability results for stochastic difference equations with constant coefficients. The topics covered are diverse, ranging from linear and nonlinear equations to delayed and both discrete and continuous types. The relevance of the theoretical concepts is illustrated through examples from physics, such as the control of an inverted pendulum and the study of epidemics. This specialized book is primarily aimed at professionals in stability theory, but it is also of interest to mathematicians and researchers dealing with pure and computational mathematical issues.