  We investigate the incremental stability properties of It\^o stochastic
dynamical systems. Specifically, we derive a stochastic version of nonlinear
contraction theory that provides a bound on the mean square distance between
any two trajectories of a stochastically contracting system. This bound can be
expressed as a function of the noise intensity and the contraction rate of the
noise-free system. We illustrate these results in the contexts of stochastic
nonlinear observers design and stochastic synchronization.
