Scaling limits and exit law for multiscale diffusions

Article type: Research Article

Authors: Almada, Sergio Angel | Spiliopoulos, Konstantinos^;

Affiliations: Department of Statistics and Operations Research, University of North Carolina, 304 Hanes Hall CB #3260, Chapel Hill, NC 27599, USA. E-mail: [email protected] | Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA 02215, USA. E-mail: [email protected]

Note: [] Corresponding author. E-mail: [email protected]

Abstract: In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law of the joint distribution of the exit time and exit location. We apply our results to the first order Langevin equation in a rough potential, studying both fluctuations around the typical behavior and the conditional limiting exit law, conditional on the rare event of going against the underlying deterministic flow.

Keywords: multiscale dynamics, small noise, Gaussian correction, exit problem, conditional rare events

DOI: 10.3233/ASY-131207

Journal: Asymptotic Analysis, vol. 87, no. 1-2, pp. 65-90, 2014