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

Antoine Lejay 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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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Antoine Lejay. A Monte Carlo estimation of the mean residence time in cells surrounded by thin layers. Mathematics and Computers in Simulation, Elsevier, 2018, Tenth IMACS Seminar on Monte Carlo Methods (MCM 2015), 143C, pp.65-77. ⟨10.1016/j.matcom.2017.05.008⟩. ⟨hal-01216471v6⟩

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