Improved Simulation Techniques for First Exit Time of Neural Diffusion Models |
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Authors: | Hasan Alzubaidi |
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Institution: | Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia |
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Abstract: | We consider the fixed and exponential time-stepping Euler algorithms, with boundary tests, to calculate the mean first exit times (MFET) of two one-dimensional neural diffusion models, represented by the Ornstein–Uhlenbeck (OU) process and a stochastic space-clamped FitzHugh–Nagumo (FHN) system. The numerical methods are described and the convergence rates for the MFET analyzed. A boundary test improves the rate of convergence from order one-half to order 1. We show how to apply the multi-level Monte Carlo (MLMC) method to an Euler time-stepping method with boundary test and this improves the Monte Carlo computation of the MFET. |
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Keywords: | Exponential time-stepping Euler algorithm First exit time FitzHugh–Nagumo model Fixed time-step Euler method Ornstein–Uhlenbeck process |
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