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...

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Veröffentlicht in:	The Annals of applied probability 2016-06, Vol.26 (3), p.1727-1742
1. Verfasser:	Lejay, Antoine
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary conditions Brownian motion Diffusion coefficient Markov processes Mathematical constants Mathematical discontinuity Mathematics Probabilities Probability Probability distribution Random variables Simulation Simulations Stochastic processes
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Beschreibung
Zusammenfassung:	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.
ISSN:	1050-5164 2168-8737
DOI:	10.1214/15-AAP1131