22: Stochastic ordering of extreme first passage times for simple neural models

Thomas M. Menino Convention & Exhibition Center 

S.E. Lawley (2020, J. Math. Biol. 80:2301-2325) and subsequent papers examined the distribution of extreme first passage times to a constant threshold for a variety of diffusion processes. He starts with an ensemble of population of identiacal diffusion processes and considers the fastest one or minimum among the population to reach the threshold. He called these "extreme first passage times". Here we use previous results on the almost sure stochastic ordering of first passage times for one dimensional diffusion processes (L. Sacerdote, C. E. Smith, 2004, Methodology and Computing in Applied Probability 6:323-341) to examine stochastic orderings in extreme first passage times for several commonly used neural integrate and fire models.

Gumbel distribution

diffusion processes

Neural models

first passage times 

Biometrics Section