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Erschienen in:
1990 | OriginalPaper | Buchkapitel
Diffusion Processes on Lie Groups and Principal Fibre Bundles
verfasst von : Ya. I. Belopolskaya, Yu. L. Dalecky
Erschienen in: Stochastic Equations and Differential Geometry
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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Let X be a smooth Banach manifold and G a group of smooth transformations of X . Sometimes we shall denote such a pair by (X, G). In this chapter, we shall deal with stochastic processes on X compatible in a certain sense with G-actions. Particular attention will be paid to the case X = G and X = P, where P is a principal fibre bundle over a certain manifold Y with G the structural group of p : P → Y. The most interesting in those two cases are equations with invariant (under actions of the group G) coefficients.