Asymptotic description of stochastic neural networks. II - Characterization of the limit law

@article{Faugeras2014AsymptoticDO,
title={Asymptotic description of stochastic neural networks. II - Characterization of the limit law},
author={O. Faugeras and J. MacLaurin},
journal={arXiv: Probability},
year={2014}
}

We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H announced there to prove that H has a unique minimum mu_e, a stationary measure on the set of trajectories. We characterize this measure by its two marginals, at time 0, and from time 1 to T. The second marginal is a stationary Gaussian measure. With an eye on applications, we show that its mean and covariance… Expand