Moser Regularization of a Stochastically Perturbed Kepler Problem

We consider a stochastic Kepler problem perturbed by a Hamiltonian noise affecting the angular momentum vector. We show that the angular momentum and the Laplace-Runge-Lenz vectors are conserved in magnitude and as a consequence, the distance and speed of the particle follow deterministic dynamics. Further, in a procedure similar to Moser's regularization, we transform the stochastic Kepler problem to obtain its dynamics as a stochastic geodesic flow on a 3-sphere.