Ito, Stratonovich and Geometry

Abstract

We revisit the impact of geometry on the evolution of stochastic differential equations in embedded Riemannian manifolds. We decompose the Ito-Stratonovich drift adjustment into a projection onto the normal space, a 'pinning' drift that keeps the process on the manifold and a tangential component. By means of some robotics examples we show how a loss of measurement information changes the drift adjustment so that an Ito-Stratonovich equivalence can be lost.