  In this paper, we propose a framework for studying the probabilistic
reachability of stochastic control systems. Given a stochastic system, we
introduce a separation strategy for reachability analysis that decouples the
effect of deterministic input/disturbance and stochastic uncertainty. A
remarkable feature of this separation strategy is its ability to leverage any
deterministic reachability framework to capture the effect of deterministic
input/disturbance. Furthermore, this separation strategy encodes the impact of
stochastic uncertainty on reachability analysis by measuring the distance
between the trajectories of the stochastic system and its associated
deterministic system. Using contraction theory, we provide probabilistic bounds
on this trajectory distance and estimate the propagation of stochastic
uncertainties through the system. By combining this probabilistic bound on
trajectory distance with two computationally efficient deterministic
reachability methods, we provide estimates for probabilistic reachable sets of
the stochastic system. We demonstrate the efficacy of our framework through
numerical experiments on a feedback-stabilized inverted pendulum.
