A probabilistic interpretation of the transmission conditions using the Skew Brownian motion
Lejay, Antoine
HAL, inria-00092418 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  Skew Brownian motion,  transmission condition,  parabolic PDE,  diffusion with singular drift,  local time,  AMS 60J60, 60H30,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{inria-00092418,
     author = {Lejay, Antoine},
     title = {A probabilistic interpretation of the transmission conditions using the Skew Brownian motion},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00092418}
}

Lejay, Antoine. A probabilistic interpretation of the transmission conditions using the Skew Brownian motion. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/inria-00092418/