1A 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 pro-cesses. The arguably dry approach is avoided of first introducing differential geometry and only then introducing stochastic pro-cesses; both areas are motivated and developed jointly. Index Terms—Differential geometry, stochastic differential equations on manifolds, estimation theory on manifolds, continuous-time stochastic processes, Ito ̂ diffusions, Brownian motion, Lie groups