The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1727-1742.
The snapping out Brownian motion
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.
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1727-1742.
Received: January 2013
Revised: July 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
Digital Object Identifier
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
Lejay, Antoine. The snapping out Brownian motion. Ann. Appl. Probab. 26 (2016), no. 3, 1727--1742. doi:10.1214/15-AAP1131. https://projecteuclid.org/euclid.aoap/1465905017