  In this era of fast and large-scale opinion formation, a mathematical
understanding of opinion evolution, a.k.a. opinion dynamics, is especially
important. Linear graph-based dynamics and bounded confidence dynamics are the
two most popular models for opinion dynamics in social networks. Recently,
stochastic bounded confidence opinion dynamics were proposed as a general
framework that incorporates both these dynamics as special cases and also
captures the inherent stochasticity and noise (errors) in real-life social
exchanges. Although these dynamics are quite general and realistic, their
analysis is particularly challenging compared to other opinion dynamics models.
This is because these dynamics are nonlinear and stochastic, and belong to the
class of Markov processes that have asymptotically zero drift and unbounded
jumps. The asymptotic behavior of these dynamics was characterized in prior
works. However, they do not shed light on their finite-time behavior, which is
often of interest in practice. We take a stride in this direction by analyzing
the finite time behavior of a two-agent system, which is fundamental to the
understanding of multi-agent dynamics. In particular, we show that the opinion
difference between the two agents is well concentrated around zero under the
conditions that lead to asymptotic stability of the dynamics.
