The snapping out Brownian motion

Antoine Lejay (1, 2)

1 TOSCA - TO Simulate and CAlibrate stochastic models
2 IECL - Institut Élie Cartan de Lorraine

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.

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

Domains: Probability [math.PR]

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