Parameter estimation via homogenization for stochastic dynamical systems with oscillating coefficients

This paper is devoted to studying parameter estimation for a class of stochastic dynamical systems with oscillating coefficients. We show that the homogenized systems faithfully capture the dynamical quantities such as mean exit time and escape probability. Exacting data from observations on the mean exit time (or escape probability) of the original systems, we try to fit the mean exit time (or escape probability) of the homogenized systems by least square method. In this way, we can accurately estimate the unknown parameter in the drift under appropriate assumptions. Furthermore, we conduct some numerical experiments to illustrate our method.