发表机构
Korteweg–de Vries Institute for Mathematics, University of Amsterdam; Institute for Informatics, University of Amsterdam; Department of Economics and Business Economics, Aarhus University; Department of Data Science and Analytics, BI Norwegian Business School; CoRE, Center for Research in Energy: Economics and Markets（阿姆斯特丹大学科特韦格-德弗里斯数学研究所; 阿姆斯特丹大学信息学研究所; 奥胡斯大学经济与商业经济系; BI挪威商学院数据科学与分析系; 能源研究中心：经济与市场）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出仿射纯跳 Volterra 场，通过稀疏化 Poisson 测度积分定义，导出仿射变换公式，推广纯跳仿射 Volterra 过程至随机场，涵盖幅值场、Hawkes 系统等特例。
AI 中文摘要
我们研究一类表现出自激聚类的非负时空随机场，称之为仿射纯跳 Volterra 场。它们通过将 Volterra 核关于一个稀疏化 Poisson 随机测度进行随机积分来定义，且稀疏化方式使得该场可表示为同一核关于另一个随机测度的随机积分，该随机测度的补偿子具有逐点仿射于场本身的密度。这一表示导致仿射变换公式，将场的泛函的 Laplace 变换刻画为确定性非线性 Volterra 积分方程的解。仿射纯跳 Volterra 随机场将非负有限一阶矩子类的纯跳仿射 Volterra 过程推广到随机场设定。该框架包含非负有限变差幅值场、标记 Hawkes 系统和分支型模型作为特例，我们通过示例明确这些联系。
英文摘要
We study a class of non-negative spatio-temporal random fields that exhibit self-exciting clustering, which we refer to as affine pure-jump Volterra fields. They are defined via stochastic integration of a Volterra kernel against a thinned Poisson random measure and the thinning is such that the field admits a representation as a stochastic integral of the same kernel, but against a random measure whose compensator has a density that is pointwise affine in the field itself. This representation leads to affine transform formulas characterizing the Laplace transform of functionals of the field up to the solution of a deterministic non-linear Volterra integral equation. Affine pure-jump Volterra random fields extend a non-negative finite-first-moment subclass of pure-jump affine Volterra processes to the random-field setting. The framework includes non-negative finite-variation ambit fields, marked Hawkes systems, and branching-type models as special cases, and we make these connections explicit through examples.
