Abstract
The factorisation of semi-martingales on finite dimensional principal fibre bundles is carried out and the specific cases of martingales diffusions and Brownian motion are considered. The factorisation of a class of diffusions including a regularised Brownian motion is investigated for fibre bundles with an infinite dimensional Hilbert manifold as total space. A relationship is set up between factorisation of stochastic processes and the Faddeev-Popov procedure.
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