A Primer on Stochastic Differential Geometry for Signal Processing

TL;DR

This paper introduces stochastic differential geometry on manifolds, combining differential geometry and stochastic processes in a unified way, aimed at signal processing applications without requiring prior specialized knowledge.

Contribution

It provides an accessible primer that jointly develops stochastic processes and differential geometry for signal processing, filling a gap for practitioners without prior expertise.

Findings

Unified framework for stochastic processes on manifolds

Accessible introduction without prior differential geometry knowledge

Application-oriented perspective 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.