Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.

中文翻译：

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随机微分方程的路径积分方法。

随机微分方程（SDE）在数学神经科学中有多种应用，而且非常困难。在这里，我们对微扰场理论和路径积分方法进行独立的教学研究，以计算SDE的概率密度函数的矩。该方法可以扩展到高维系统，例如耦合神经元的网络，甚至具有猝灭性疾病的确定性系统。