Geodesic random walks, diffusion processes and Brownian motion on Finsler manifolds

TL;DR

This paper demonstrates that geodesic random walks on complete Finsler manifolds with bounded geometry converge to a diffusion process resembling Brownian motion, adjusted by a drift related to a Riemannian metric.

Contribution

It establishes the convergence of geodesic random walks on Finsler manifolds to a specific diffusion process, linking Finsler geometry with stochastic analysis.

Findings

Geodesic random walks converge to a diffusion process.

The limiting process is a drift-adjusted Brownian motion.

Results connect Finsler and Riemannian geometric stochastic processes.

Abstract

We show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.