In this paper, we present a survey of recent progress on the emergent behaviors of stochastic particle models which arise from the modeling of collective dynamics. Collective dynamics of interacting autonomous agents is ubiquitous in nature, and it can be understood as a formation of concentration in a state space. The jargons such as aggregation, herding, flocking and synchronization describe such concentration phenomena. Recently it became one of the emerging topics in the applied mathematics community due to possible engineering applications and close relation with nonlocal partial differential equations. When an autonomous agent system interacts with unknown environment as an open system, the effects of hidden and unidentified interactions between the environment and the autonomous system are often realized by stochastic noises in agent dynamics, and the temporal evolution of the autonomous system results in stochastic collective models. From the viewpoint of dynamical systems theory, it is very interesting how collective dynamics emerges from initial state. As concrete examples, we consider four specific stochastic collective models (stochastic Winfree and Kuramoto models for synchronization, the stochastic Cucker–Smale model for flocking, and a first-order stochastic nonlinear consensus model), and we also briefly review the state-of-the-art results for these models on the emergence of collective dynamics and discuss their applications in finance and optimization.

在本文中，我们介绍了对集体动力学建模产生的随机粒子模型的涌现行为的最新进展的调查。相互作用的自主主体的集体动力学在自然界中无处不在，可以理解为状态空间中浓度的形成。聚集、成群、聚集和同步等行话描述了这种集中现象。由于可能的工程应用以及与非局部偏微分方程的密切关系，它最近成为应用数学界的新兴课题之一。当自治代理系统作为一个开放系统与未知环境交互时，环境与自治系统之间隐藏和未识别的相互作用的影响通常通过代理动力学中的随机噪声来实现，而自治系统的时间演化导致随机集体模型。从动力系统理论的角度来看，集体动力如何从初始状态出现是非常有趣的。作为具体示例，我们考虑了四种特定的随机集体模型（用于同步的随机 Winfree 和 Kuramoto 模型，用于植绒的随机 Cucker-Smale 模型，以及一阶随机非线性共识模型），我们还简要回顾了状态 -这些模型关于集体动力出现的最先进结果，并讨论它们在金融和优化方面的应用。自治系统的时间演化导致随机集体模型。从动力系统理论的角度来看，集体动力如何从初始状态出现是非常有趣的。作为具体示例，我们考虑了四种特定的随机集体模型（用于同步的随机 Winfree 和 Kuramoto 模型，用于植绒的随机 Cucker-Smale 模型，以及一阶随机非线性共识模型），我们还简要回顾了状态 -这些模型关于集体动力出现的最先进结果，并讨论它们在金融和优化方面的应用。自治系统的时间演化导致随机集体模型。从动力系统理论的角度来看，集体动力如何从初始状态出现是非常有趣的。作为具体示例，我们考虑了四种特定的随机集体模型（用于同步的随机 Winfree 和 Kuramoto 模型，用于植绒的随机 Cucker-Smale 模型，以及一阶随机非线性共识模型），我们还简要回顾了状态 -这些模型关于集体动力出现的最先进结果，并讨论它们在金融和优化方面的应用。