On exponential stability of difference stochastic systems

The paper is concerned with extension of the notions of an exponential $p$-stabi­ lity and exponential $q$-instability to the case of difference stochastic systems with random initial conditions. Sufficient conditions for exponential $p$-stability and $q$-instability are given both for the mean and a probability of 1. The findings are illustrated with examples of specific stochastic difference systems.