We investigate the incremental stability properties of Ito 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 nonlinear observers design and stochastic synchronization.
No takes yet. Share an insight, caveat, or question.
Pham et al. (2009) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: