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Journal Articles The Annals of Applied Probability Year : 2016

The snapping out Brownian motion

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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Dates and versions

hal-00781447 , version 1 (26-01-2013)
hal-00781447 , version 2 (06-01-2015)
hal-00781447 , version 3 (09-07-2015)
hal-00781447 , version 4 (03-08-2015)

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Cite

Antoine Lejay. The snapping out Brownian motion. The Annals of Applied Probability, 2016, 26 (3), pp.1727-1742. ⟨10.1214/15-AAP1131⟩. ⟨hal-00781447v4⟩
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