英文标题：
《At the Mercy of the Common Noise: Blow-ups in a Conditional
McKean--Vlasov Problem》
---
作者：
Sean Ledger and Andreas Sojmark
---
最新提交年份：
2021
---
英文摘要：
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up\' phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean--Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean--Vlasov problem, which can be realised as limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise.
---
中文摘要：
通过引入由布朗运动驱动的公共噪声源，我们在大平均场系统中推广了一个正反馈和传染模型。尽管驾驶动力是连续的，但正反馈效应可能会导致“爆炸”现象，从而导致解决方案产生跳跃不连续性。我们的主要结果是双重的，涉及模型的条件McKean-Vlasov公式。首先，我们证明了这个McKean-Vlasov问题有全局解，它可以作为具有共同噪声的激励粒子系统的极限点来实现。此外，我们得出了爆破发生的结果，从而说明了如何通过路径实现公共噪声来触发或防止这些事件。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->