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Averaging dynamics driven by fractional Brownian motion
| File | Description | Size | Format | |
|---|---|---|---|---|
 Averaging.pdf | Accepted version | 476.31 kB | Adobe PDF | View/Open |
| Title: | Averaging dynamics driven by fractional Brownian motion |
| Authors: | Hairer, M Li, X-M |
| Item Type: | Journal Article |
| Abstract: | We consider slow / fast systems where the slow system is driven by fractionalBrownian motion with Hurst parameterH >12. We show that unlike in the caseH=12, convergence to the averaged solution takes place in probability and thelimiting process solves the ‘naïvely’ averaged equation. Our proof strongly relieson the recently obtained stochastic sewing lemma. |
| Issue Date: | 1-Jul-2020 |
| Date of Acceptance: | 1-Oct-2019 |
| URI: | http://hdl.handle.net/10044/1/74390 |
| DOI: | 10.1214/19-AOP1408 |
| ISSN: | 0091-1798 |
| Publisher: | Institute of Mathematical Statistics |
| Start Page: | 1826 |
| End Page: | 1860 |
| Journal / Book Title: | Annals of Probability |
| Volume: | 48 |
| Issue: | 4 |
| Copyright Statement: | © Institute of Mathematical Statistics, 2020 |
| Sponsor/Funder: | The Leverhulme Trust Commission of the European Communities |
| Funder's Grant Number: | RL-2012-020-Transfer In 615897 |
| Keywords: | Statistics & Probability 0101 Pure Mathematics 0104 Statistics |
| Publication Status: | Published |
| Online Publication Date: | 2020-07-20 |
| Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |