Convergence of solutions of SDEs to Harris flows

M. B. Vovchanskii
Theory of Stochastic Processes
Vol.23 (39), no.2, 2018, pp.80-91
A method of the approximation of a coalescing Harris flow with homeomorphic stochastic flows built as solutions to SDEs w.r.t. continuous martingales with spatial parameters in the sense of Kunita is proposed. The joint convergence of forward and backward flows as diffusions is obtained, as well as the joint convergence of forward and backward transformations of the real axe under the action of the flows.