Geometric Ergodicity of a Hypoelliptic Diffusion Modelling The Melt-Spinning Process of Nonwoven Materials

摘要

We analyze the large time behavior of a stochastic model for the lay-down offibers on a conveyor belt in the production process of nonwovens. It is shown,that under weak conditions this degenerate diffusion process is strong mixing,confirming a conjecture of Grothaus and Klar. Moreover, under some additionalassumptions even geometric ergodicity is established using probabilistic tools-- described in the book of Meyn and Tweedie -- in combination with methodsfrom stochastic analysis.