Decomposition of stochastic flows with automorphism of subbundles component

Abstract

We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $ph{i}_t$ by $G(M)$, in the sense that ${\varphi }_t={\xi }_t\circ {\rho }_t$ where ${\xi }_t\in G(M)$, the remainder ${\rho }_t$ has derivative which is vertical but transversal to the fibre of $P$. This geometrical context generalizes previous results where $M$ is a Riemannian manifold and ${\varphi }_t$ is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on $M$.

To appear in Stochastics and Dynamics, 2012

Cited by in corpus (1)

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