Homogenization of Dissipative, Noisy, Hamiltonian Dynamics

Jeremiah Birrell, Jan Wehr

Published 2016-08-29Version 1

We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a noise-induced drift term. We prove convergence to the solution of the homogenized equation in an $L^p$-norm.