Recently I've read a paraphrasing from Ito saying that he sometimes thinks of martingales as Geodesics in a very large dimensional manifold.

My question is, is there any research studying this idea? Moreover are there any papers linking differential geometry to stochastic Calculus?

Any links would be greatly appreciated.

Recently I've read a paraphrasing from Ito saying that he sometimes thinks of martingales as geodesics in a very large dimensional manifold.

My question is, is there any research studying this idea? Moreover are there any papers linking differential geometry to stochastic Calculus?

Any links would be greatly appreciated.