TY - JOUR
T1 - Improved simulation techniques for first exit time of neural diffusion models
AU - Alzubaidi, H.
AU - Shardlow, T.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84902670004&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1080/03610918.2012.755197
U2 - 10.1080/03610918.2012.755197
DO - 10.1080/03610918.2012.755197
M3 - Article
AN - SCOPUS:84902670004
SN - 0361-0918
VL - 43
SP - 2508
EP - 2520
JO - Communications in Statistics - Simulation and Computation
JF - Communications in Statistics - Simulation and Computation
IS - 10
ER -