We present a simple uniqueness argument for a collection of McKean–Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak feedback we mean the case where the contagion parameters are small enough to prevent blow‐ups in solutions. Next, we specialise to a Brownian driver and show how the same techniques can be extended to give short‐time uniqueness after blow‐ups, regardless of the feedback strength, by exploiting a localised form of weak feedback. The heart of our approach is a surprisingly simple probabilistic comparison argument that is robust in the sense that it does not ask for any regularity of the solutions.

中文翻译：

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弱反馈状态下具有传染性的McKean-Vlasov系统的唯一性

对于最近已引起关注的McKean-Vlasov问题，我们提出了一个简单的唯一性论证。我们的第一个结果表明，在弱反馈机制下，非常通用的随机驱动程序类具有全局唯一性。弱反馈是指传染参数足够小以防止溶液爆炸的情况。接下来，我们专门研究布朗驱动程序，并展示如何利用局部反馈的弱化形式，将相同的技术扩展到爆裂后的短时唯一性，而不管反馈强度如何。我们的方法的核心是一个令人惊讶的简单概率比较论证，该论证在不要求解决方案有任何规律性的意义上是稳健的。