  We study a stochastic equation modeling the lay-down of fibers in the
production process of nonwovens. The equation can be formulated as some
manifold-valued Stratonovich stochastic differential equation. Especially, we
study the long time behaviour of the stochastic process. Demanding mathematical
difficulties arising due to the degeneracity of the lay-down equation and its
associated generator. We prove strong mixing properties by making use of the
hypoellipticity of the generator and a new version of Doob's theorem derived
recently by Gerlach and Nittka. Moreover, we show convergence to equilibrium
exponentially fast with explicitly computable rate of convergence. This
analytic approach uses powerful modern Hilbert space methods from the theory of
hypocoercivity developed by Dolbeault, Mouhot and Schmeiser. Summarizing, we
give interesting mathematical applications of geometric stochastic analysis to
real world problems.
