The Library
Homogenization for deterministic maps and multiplicative noise
Tools
Tools
Tools
Gottwald, G. A. and Melbourne, Ian (2013) Homogenization for deterministic maps and multiplicative noise. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 469 (Number 2156). Article number 20130201. doi:10.1098/rspa.2013.0201 ISSN 1364-5021.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1098/rspa.2013.0201
Abstract
A recent paper of Melbourne & Stuart (2011 A note on diffusion limits of chaotic skew product flows. Nonlinearity 24, 1361-1367 (doi:10.1088/0951-7715/24/4/018)) gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential equation with additive noise. In contrast to other approaches, the assumptions on the fast flow are very mild. In this paper, we extend this result from continuous time to discrete time. Moreover, we show how to deal with one-dimensional multiplicative noise. This raises the issue of how to interpret certain stochastic integrals; it is proved that the integrals are of Stratonovich type for continuous time and neither Stratonovich nor It (o) over cap for discrete time. We also provide a rigorous derivation of super-diffusive limits where the stochastic differential equation is driven by a stable Levy process. In the case of one-dimensional multiplicative noise, the stochastic integrals are of Marcus type both in the discrete and continuous time contexts
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||
| Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||
| Publisher: | The Royal Society Publishing | ||||
| ISSN: | 1364-5021 | ||||
| Official Date: | 8 August 2013 | ||||
| Dates: |
|
||||
| Volume: | Volume 469 | ||||
| Number: | Number 2156 | ||||
| Page Range: | Article number 20130201 | ||||
| DOI: | 10.1098/rspa.2013.0201 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
