Reference request for stochastic processes on manifolds

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I'm looking for some references on stochastic processes on manifolds. The more introductory the better. Thanks.

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Check out "Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing" by Pierre Henry-Labord$\grave{\text{e}}$re. While this book is very focused on applications, it has an interesting blend of both advanced ideas in manifold theory (connections on vector bundles) as well probability and stochastic processes. The only unfortunate part is that I can't say this book is all that axiomatic, but if you're somewhat comfortable with both subjects that this might give you one avenue to start integrating ideas from both.