具有相互作用粒子系统的随机局部强度损失模型

Mean field limits for interacting Hawkes processes in a diffusive regime

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random measures. We show that, as the number of interacting components N tends to infinity, this intensity converges in distribution in Skorohod space to a CIR-type diffusion. Moreover, we prove the convergence in distribution of the Hawkes processes to the limit point process having the limit diffusion as intensity. To prove the convergence results, we use analyti…

气候不确定性下的超额损失再保险和巨灾债券定价：基于温度依赖随机强度的Cox过程框架

Pricing Excess-of-Loss Reinsurance and CAT Bonds under Climate Uncertainty: A Cox Process Framework with Temperature-Dependent Stochastic Intensity

提出气候感知的Cox过程定价框架，通过温度依赖的随机强度建模非平稳巨灾风险，蒙特卡洛模拟显示气候依赖显著影响定价，且基准模型可能低估经济资本需求约13.7%。

具有衰减空间密度的孔洞的无限膜的张力损失

The Loss of Tension in an Infinite Membrane with Holes of Decaying Spatial Density

研究非均匀泊松点过程下随机孔洞对无限膜张力的影响，给出张力完全损失与不损失的相变条件。

完美模拟相互作用的点过程、损失网络和伊辛模型

Perfect simulation for interacting point processes, loss networks and Ising models

本文给出了一个关于泊松过程绝对连续的测度的完美模拟算法，这些测度可以作为生灭过程的不变测度得到。例子包括面积和周长相互作用点过程（随机颗粒），损失网络的不变测度，伊辛轮廓和随机簇模型。该算法不涉及耦合的过程与不同的初始条件，它是不绑在单调性要求。此外，它直接提供了无限体积测量的有限窗口的完美样本，受到时间和空间“用户不耐烦偏差”的影响。该算法是基于一个两步的过程：（i）一个完美的模拟计划（有限的和随机的）相关部分的（时空）标记泊松过程（自由生灭过程，自由损失网络），和（ii）"清洗“算法，修剪出这个过程根据目标过程的相互作用规则。第一步涉及完美生成给定对象的“祖先”，即可能对目标进程下的出生率产生影响的前身。如果这些“祖先”形成概率为1的有限集，那么第二步，也就是整个过程是可行的。我们提出了一个充分的标准，这个条件的基础上，没有无限的集群相关联的（向后）导向的渗流模型。

Persistence in a large network of locally interacting neurons

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers an instantaneous increase in electric potential to a fixed number of randomly chosen neurons. We prove that, as the number of neurons approaches infinity, the finite network converges to a nonlinear meanfield process characterised by a jump-type stochastic differential equation. We show that this process displays a phase transition: the activity of a typical …