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.
Citation
Antoine Lejay. "The snapping out Brownian motion." Ann. Appl. Probab. 26 (3) 1727 - 1742, June 2016. https://doi.org/10.1214/15-AAP1131
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