Well-posedness of the stochastic neural field equation with discontinuous firing rate

作者：Krueger J.^*; Stannat W.

来源：Journal of Evolution Equations, 2018, 18(2): 515-547.

DOI：10.1007/s00028-017-0409-z

We study the existence and uniqueness of mild solutions to the deterministic and the stochastic neural field equation with Heaviside firing rate. Since standard well-posedness results do not apply in case of a discontinuous firing rate, we present a monotone Picard iteration scheme to show the existence of a maximal mild solution. Further, we illustrate that general uniqueness does not hold, and therefore investigate uniqueness under suitable additional properties of the solutions. Here a novel criterion, the so-called absolute continuity condition is introduced. Moreover, we observe regularisation by noise: with a suitable choice of spatially correlated additive noise uniqueness is restored without imposing any additional structural assumptions.

• 出版日期2018-6