A probabilistic interpretation of the transmission conditions using the Skew Brownian motion

Antoine Lejay 1, 2
1 IECN - Institut Élie Cartan de Nancy
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : In order to solve with a Monte Carlo method a parabolic (or elliptic) PDE with a transmission condition, we need to understand the behavior of the stochastic process when it reaches a point where this tranmission condition holds. In this article, we show that a process called the Skew Brownian motion can be helpful to understand how to deal with this kind of problem in a one-dimensional media.
Keywords : Skew Brownian motion transmission condition parabolic PDE diffusion with singular drift local time
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Conference papers
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Antoine Lejay. A probabilistic interpretation of the transmission conditions using the Skew Brownian motion. Multi Scale problems and asymptotic analysis - Narvik Midnight Sun Conference 2004, European Research Training Network Homogenization and Multiple Scales (HMS2000)., 2004, Narvik Norvège. ⟨inria-00092418⟩

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