The snapping out Brownian motion
Probability
2016-06-28 v1
Abstract
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier. For this, we use a process called here the snapping out Brownian motion, whose properties are studied. As this construction is motivated by applications, for example, in brain imaging or in chemistry, a simulation scheme is also provided.
Cite
@article{arxiv.1606.08230,
title = {The snapping out Brownian motion},
author = {Antoine Lejay},
journal= {arXiv preprint arXiv:1606.08230},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AAP1131 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)