The Annals of Applied Probability

The snapping out Brownian motion

Antoine Lejay

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 3 (2016), 1727-1742.

Received: January 2013
Revised: July 2015
First available in Project Euclid: 14 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60G20: Generalized stochastic processes 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J55: Local time and additive functionals

Interface condition elastic Brownian motion semi-permeable barrier thin layer piecing out a Markov process


Lejay, Antoine. The snapping out Brownian motion. Ann. Appl. Probab. 26 (2016), no. 3, 1727--1742. doi:10.1214/15-AAP1131.

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