Wiener Process with Reflection in Non-Smooth Narrow Tubes
Konstantinos Spiliopoulos, Brown University
Abstract
Wiener process with instantaneous reflection in narrow tubes of
width ε<<1 around axis x is considered
in this paper.
The tube is assumed to be (asymptotically) non-smooth in the
following sense.
Let Vε(x) be the volume of the
cross-section of the tube. We assume that
(1/ε)Vε(x) converges in an appropriate
sense to a non-smooth function as
ε->0. This limiting function can be composed by smooth
functions, step functions and also the Dirac delta
distribution. Under this assumption we prove that the
x-component of the Wiener process converges weakly to a
Markov
process that behaves like a standard diffusion process away from the
points of discontinuity and has to
satisfy certain gluing conditions at the
points of discontinuity.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.