The Sharma-Parthasarathy stochastic two-body problem
  We study the Sharma-Parthasarathy stochastic two-body problem introduced by N. Sharma and H. Parthasarathy in \cite{sharma}. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case. 
Jacky Cresson, Fr\'ed\'eric Pierret, B\'en\'edicte Puig
math-ph astro-ph.EP math.MP