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arXiv · 1606.08230

The snapping out Brownian motion

Antoine Lejay
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Abstract

We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ 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.

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Antoine Lejay. 2016-06-27. The snapping out Brownian motion. https://doi.org/10.1214/15-aap1131

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