I am doing a project in stochastic differential geometry mainly(Brownian motion on manifolds) ,the proof of laplacian-beltrami operator. I am currently reading williams "diffusions and markov process" and i want to get book recommendation, so that i can go through this text easily .i am currently reading stochastic process by jazwinski .i also want to know from where i should read the geometry part of it.
Here are a few things to look at. Elton Hsu has a brief intro here
He also has a old paper published by the AMS
Both of these have a nice list of references.
As far as books in print I would recommend An Introduction to the Analysis of Paths on a Riemannian Manifold by Stroock which is also published by the AMS. You may also want to look at Stochastic Differential Equations and Diffusion Processes by Wantanabe. His book not only has a nice intro to stochastic calculus, but it also has a few chapters on diffusion processes on a manifold.