Convergence of solutions of SDEs to Harris flows

TL;DR

This paper introduces a new method to approximate Harris flows using SDEs driven by continuous martingales, demonstrating joint convergence of forward and backward flows and transformations.

Contribution

It proposes a novel approximation technique for Harris flows via SDEs with continuous martingales, establishing convergence results for both forward and backward flows.

Findings

Established joint convergence of forward and backward flows.

Demonstrated convergence of transformations of the real axis under the flows.

Provided a new approximation method for Harris flows using SDEs.

Abstract

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.