Large Deviations for Nonlocal Stochastic Neural Fields

@inproceedings{Kuehn2014LargeDF,
  title={Large Deviations for Nonlocal Stochastic Neural Fields},
  author={Christian Kuehn and Martin G. Riedler},
  booktitle={Journal of mathematical neuroscience},
  year={2014}
}
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional… CONTINUE READING