Langevin equation in the small mass limit: higher order approximations

We study the Langevin equation describing the motion of a particle of mass m in a potential and/or magnetic field, with state-dependent drift and diffusion. We develop a hierarchy of approximate equations for the position degrees of freedom that achieve accuracy of order m^{k/2} over finite time intervals for any positive integer k. This extends the previous work in which effective equations for the position variables were derived in the limit when the mass goes to zero. This is a joint work with Jeremiah Birrell.