  In this paper, we develop a novel contraction framework for stability
analysis of discrete-time nonlinear systems with parameters following
stochastic processes. For general stochastic processes, we first provide a
sufficient condition for uniform incremental exponential stability (UIES) in
the first moment with respect to a Riemannian metric. Then, focusing on the
Euclidean distance, we present a necessary and sufficient condition for UIES in
the second moment. By virtue of studying general stochastic processes, we can
readily derive UIES conditions for special classes of processes, e.g., i.i.d.
processes and Markov processes, which is demonstrated as selected applications
of our results.
