Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.

翻译：分布依赖型随机动力系统在工程与科学领域广泛存在。本文考虑一类此类系统，该系统建模了在具有随机涨落的向量场中相互作用粒子的极限行为。我们的目标是考察向量场平衡稳态之间的最概然迁移路径。在小噪声条件下，作用泛函不涉及描述未受扰动确定性流的骨架方程解，该流由零距离相互作用移位的向量场所生成。因此，我们转而研究无分布依赖性的随机微分方程的最概然迁移路径。这使得我们可以通过自适应最小作用方法计算这类分布依赖型随机动力系统的最概然迁移路径，并通过两个算例阐明该方法。