Browsing by Subject "Perturbations"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
    (Springer, 2015) Hottovy, S.; McDaniel, A.; Wehr, J.; Volpe, G.
    We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein-Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.