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

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

2011-12-28

arxiv.org/abs/1112.6159v1

Mathematics

Probability

23 pages

Scientific paper

We analyze the large time behavior of a stochastic model for the lay-down of fibers 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 additional assumptions even geometric ergodicity is established using probabilistic tools -- described in the book of Meyn and Tweedie -- in combination with methods from stochastic analysis.

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