  We consider the problem of adaptive stabilization for discrete-time,
multi-dimensional linear systems with bounded control input constraints and
unbounded stochastic disturbances, where the parameters of the true system are
unknown. To address this challenge, we propose a certainty-equivalent control
scheme which combines online parameter estimation with saturated linear
control. We establish the existence of a high probability stability bound on
the closed-loop system, under additional assumptions on the system and noise
processes. Finally, numerical examples are presented to illustrate our results.
