Hairer, Martin and Manson, Charles. (2010) Periodic homogenization with an interface : the one-dimensional case. Stochastic Processes and their Applications, Vol.120 (No.8). pp. 1589-1605. ISSN 0304-4149

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Abstract

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite Interface region'. The question investigated in this article is the limiting long time/large scale behaviour of such a process under diffusive rescaling. Our main result is that it converges weakly to a rescaled version of skew Brownian motion, with parameters that can be given explicitly in terms of the coefficients of the original diffusion. Our method of proof relies on the framework provided by Freidlin and Wentzell (1993) [6] for diffusion processes on a graph in order to identify the generator of the limiting process. The graph in question consists of one vertex representing the interface region and two infinite segments corresponding to the regions on either side. (C) 2010 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Stochastic Processes and their Applications
Publisher:	Elsevier Science BV
ISSN:	0304-4149
Date:	August 2010
Volume:	Vol.120
Number:	No.8
Number of Pages:	17
Page Range:	pp. 1589-1605
Identification Number:	10.1016/j.spa.2010.03.016
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Royal Society (Great Britain), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/D071593/1 (EPSRC)
URI:	http://wrap.warwick.ac.uk/id/eprint/5594

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