A Primer on Stochastic Differential Geometry for Signal Processing

Abstract

This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Ito diffusions) can be defined and studied on manifolds. No knowledge is assumed of either differential geometry or continuous-time processes. The arguably dry approach is avoided of first introducing differential geometry and only then introducing stochastic processes; both areas are motivated and developed jointly.

19 pages

References in corpus (2)

• Differential equations driven by rough paths: an approach via discrete approximation
• A Simple Proof of the Bichteler-Dellacherie Theorem

Cited by in corpus (2)

• Geometric Characteristics of Wasserstein Metric on SPD(n)
• Random Lie Brackets that Induce Torsion: A Model for Noisy Vector Fields