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

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  • Lejay, Antoine

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.

Suggested Citation

  • Lejay, Antoine, 2018. "A Monte Carlo estimation of the mean residence time in cells surrounded by thin layers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 65-77.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:65-77
    DOI: 10.1016/j.matcom.2017.05.008
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    References listed on IDEAS

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    1. Lejay, Antoine & Maire, Sylvain, 2007. "Computing the principal eigenvalue of the Laplace operator by a stochastic method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 351-363.
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