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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.

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  • $\begingroup$ Not sure what you mean by "stochastic differential geometry". Maybe you want to look at something like Differential Geometry and Statistics by Murray and Rice. Geometrical Foundations of Asymptotic Inference by Kass is also good. $\endgroup$ – Wintermute Oct 5 '15 at 13:35
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    $\begingroup$ Brownian motion on a riemannian manifold. $\endgroup$ – Nebo Alex Oct 5 '15 at 13:47
  • $\begingroup$ @Wintermute Both deal with the ways to use differential geometry as a framework to study statistical models and are offtopic here. $\endgroup$ – Did Oct 5 '15 at 14:06
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Here are a few things to look at. Elton Hsu has a brief intro here

https://www.math.kyoto-u.ac.jp/probability/sympo/PSS03abstract.pdf

He also has a old paper published by the AMS

http://www.math.northwestern.edu/~ehsu/Brownian%20Motion%20and%20Riemannian%20Geometry.pdf

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.

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