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.Comment: Published at http://dx.doi.org/10.1214/15-AAP1131 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
