Moment stability of stochastic processes with applications to control systems

We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with state-dependent restriction centered conditional process. They, in particular, generalize main result [22] which requires constant bound averaged one-step jumps The feature our make them suitable large class multiplicative-noise Under additional assumption Markovian property, we prove ergodicity that do not rely minorization condition typically needed ergodic theorems. Several applications to iterative systems, control and other dynamical systems multiplicative noise are included, these illustrative examples demonstrate wide applicability results.