  This paper studies stochastic stability of a class of discrete-time
phase-coupled oscillators. We introduce the two new notions of stochastic and
ultimate stochastic phase-cohesiveness using the concepts of Harris and
positive Harris recurrent Markov chains. Stochastic phase-cohesiveness of
oscillators in two types of networks are studied. First, oscillators in a
network with an underlying connected topology subject to both multiplicative
and additive stochastic uncertainties are considered. Second, we study a
special case of the former problem by assuming that the multiplicative
uncertainties are governed by the Bernoulli process representing the well known
Erd{\H o}s R\'enyi network.
