DECOMPOSITION OF STOCHASTIC FLOWS IN MANIFOLDS WITH COMPLEMENTARY DISTRIBUTIONS

作者：Catuogno Pedro J; Da Silva Fabiano B; Ruffino Paulo R^*

来源：Stochastics and Dynamics, 2013, 13(4): 1350009.

DOI：10.1142/S0219493713500093

• Stochastic flows
• smooth distributions
• decomposition of flows
• group of diffeomorphisms

Let M be a differentiable manifold endowed locally with two complementary distributions, say horizontal and vertical. We consider the two subgroups of (local) diffeo-morphisms of M generated by vector fields in each of of these distributions. Given a stochastic flow.t of diffeomorphisms of M, in a neighbourhood of an initial condition, up to a stopping time we decompose phi(t) = xi(t)o psi(t) where the first component is a diffusion in the group of horizontal diffeomorphisms and the second component is a process in the group of vertical diffeomorphisms. Further decomposition will include more than two components; it leads to a maximal cascade decomposition in local coordinates where each component acts only in the corresponding coordinate.

• 出版日期2013-12