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