Geometric Ergodicity of a Hypoelliptic Diffusion Modelling The Melt-Spinning Process of Nonwoven Materials
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2011
- DOI:
- 10.48550/arXiv.1112.6159
- arXiv:
- arXiv:1112.6159
- Bibcode:
- 2011arXiv1112.6159K
- Keywords:
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- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- Mathematics - Spectral Theory;
- 60J05;
- 60J60;
- 37A25;
- 37A30 (Primary) 35H10;
- 60J70 (Secondary)
- E-Print:
- 23 pages