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Wiener Process with Reflection in Non-Smooth Narrow Tubes


 
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1. Title Title of document Wiener Process with Reflection in Non-Smooth Narrow Tubes
 
2. Creator Author's name, affiliation, country Konstantinos Spiliopoulos; Brown University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Narrow Tubes; Wiener Process; Reflection; Non-smooth Boundary; Gluing Conditions; Delay
 
3. Subject Subject classification 60J60, 60J99, 37A50
 
4. Description Abstract Wiener process with instantaneous reflection in narrow tubes of width $\epsilon\ll 1$ around axis $x$ is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let $V^{\epsilon}(x)$ be the volume of the cross-section of the tube. We assume that $\frac{1}{\epsilon}V^{\epsilon}(x)$ converges in an appropriate sense to a non-smooth function as $\epsilon\downarrow 0$. 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-09-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/691
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-691
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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