Front propagation in stochastic neural fields: notes and corrections

(b) In our original analysis of spontaneous fronts (section 2.2), we required that ∆(t) = O( ), and Taylor expanded with respect to ∆(t). The correct condition is d∆(t) = O( ). Since ∆(t) turns out to be a Wiener process, this means that d∆(t) is distributed according to a Gaussian and could take on arbitrarily large values. However, for weak noise the probability that this occurs is exponentially small and we ignore such rare events in our perturbation analysis. (See sections 12.1 and 12.2 of [3] for a discussion of large deviation theory applied to traveling waves solutions.)