Mathematics – Probability
Scientific paper
2012-03-20
Mathematics
Probability
Scientific paper
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.
Grothaus Martin
Klar Axel
Maringer Johannes
Stilgenbauer Patrik
No associations
LandOfFree
Geometry, mixing properties and hypocoercivity of a degenerate diffusion arising in technical textile industry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometry, mixing properties and hypocoercivity of a degenerate diffusion arising in technical textile industry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry, mixing properties and hypocoercivity of a degenerate diffusion arising in technical textile industry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496505