Mattingly, J. C. and Stuart, A. M. (2002) Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions. Markov Processes And Related Fields, 8 (2). pp. 199-214. ISSN 1024-2953. https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320
![[img]](https://authors.library.caltech.edu/style/images/fileicons/application_pdf.png) |
PDF
- Submitted Version
See Usage Policy. 196kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320
Abstract
Two degenerate SDEs arising in statistical physics are studied. The first is a Langevin equation with state-dependent noise and damping. The second is the equation of motion for a particle obeying Stokes' law in a Gaussian random field; this field is chosen to mimic certain features of turbulence. Both equations are hypo-elliptic and smoothness of probability densities may be established. By developing appropriate Lyapunov functions and by studying the necessary control problems, geometric ergodicity is proved.
| Item Type: | Article | ||||||
|---|---|---|---|---|---|---|---|
| Related URLs: |
| ||||||
| Additional Information: | © 2002 Markov Processes and Related Fields. Supported by the National Science Foundation under grant DMS-9971087. We would like to thank Des Higham, and Wilhelm Huisinga for helpful input. | ||||||
| Funders: |
| ||||||
| Subject Keywords: | geometric ergodicity, stochastic differential equations, Langevin equation, synthetic turbulence, hypoelliptic and degenerate diffusions | ||||||
| Other Numbering System: |
| ||||||
| Issue or Number: | 2 | ||||||
| Record Number: | CaltechAUTHORS:20170613-125012320 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 78164 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 13 Jun 2017 20:02 | ||||||
| Last Modified: | 03 Oct 2019 18:06 |
Repository Staff Only: item control page
