DECOMPOSITION OF STOCHASTIC FLOWS WITH AUTOMORPHISM OF SUBBUNDLES COMPONENT

Abstract

We show that given a G-structure P on a differential manifold M, if the group G(M) of automorphisms of P is large enough, then there exists the quotient of a stochastic flows φt by G(M), in the sense that φt = ξt ◦ ρt where ξt ∈ G(M), the remainder ρt has derivative which is vertical, transversal to the fibres of P. This geometrical context generalises previous results where M is a Riemannian manifold and φt is decomposed with an isometric component, see [12] and [15], which in our context corresponds to the particular case of an SO(n) -structure on M.