A Monte Carlo estimation of the mean residence time in cells surrounded by thin layers
Résumé
We present a new Monte Carlo method to estimate the mean-residence time
of a diffusive particle in a domain surrounded by a thin layer of low diffusivity.
Through a homogenization technique, the layer is identified with a
membrane. The simulations use a stochastic process called the snapping out Brownian
motion the density of which matches suitable transmission conditions at the membrane.
We provide a benchmark test which is a simplified form of a real-life problem
coming from brain imaging techniques. We also provide a new algorithm to adaptively estimate the
exponential rate of the tail of the distribution function of the probability to be in
the domain using Monte Carlo simulations.
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