Improved simulation techniques for first exit time of neural diffusion models

H. Alzubaidi, T. Shardlow

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
166 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)2508-2520
Number of pages13
JournalCommunications in Statistics - Simulation and Computation
Volume43
Issue number10
Early online date24 Sep 2013
DOIs
Publication statusPublished - 2014

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