On the tangent flow of a stochastic differential equation with fast drift (Q2701659)

The author investigates the behavior of the tangent flow of a stochastic differential equation (SDE) with a fast drift. The state space of SDE is the two-dimensional cylinder. The fast drift has closed orbits, and it is assumed that the orbit times vary nontrivially with the axial coordinate. The effect of an infinitesimally small perturbation of the initial condition upon the trajectories of SDE which is amenable to stochastic averaging is studied. Under a nondegeneracy assumption, the rate of growth of the tangent flow is found. The calculations involve a transformation introduced by Pinsky and Wihstutz.