Improved Simulation Techniques for First Exit Time of Neural Diffusion Models

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 analysed. A boundary test improves the rate of convergence from order one half to order one. 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.