A Monte Carlo estimation of the mean residence time in cells surrounded by thin layers

•Presents a probabilistic interpretation of diffusion in medium with a thin layer of low diffusivity.•Tests the model to compute the mean-residence time in a brain imaging problem.•Improves the method for estimating an exponential rate from some distribution function estimated by a Monte Carlo method.

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.