单变量标记Hawkes过程的多变量表示
Multivariate Representations of Univariate Marked Hawkes Processes
AI总结：
本文探讨了单变量标记Hawkes过程与多变量Hawkes过程之间的联系，提出多变量无标记表示用于参数化单变量标记过程，并展示了其在不同数据上的灵活推断能力。
摘要：
单变量标记Hawkes过程被用于建模地震余震序列、传染病传播、社交媒体内容扩散和订单簿动态等现实现象。本文阐明了单变量标记Hawkes过程与多变量Hawkes过程之间的基本联系。利用这一联系，可以构建一个框架，用于在多样化数据上进行表达性强且灵活的推断。具体而言，引入了多变量无标记Hawkes表示作为参数化单变量标记Hawkes过程的工具。我们证明了此类多变量表示可以渐近逼近一大类单变量标记Hawkes过程，且在所逼近的过程是平稳的情况下也是平稳的，并且由此产生的条件强度参数是可识别的。一项模拟研究展示了该方法的有效性，并提供了由于多变量Hawkes过程相对较大的参数空间所引起误差的启发式界限。
英文摘要：
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper illustrates a fundamental connection between univariate marked Hawkes processes and multivariate Hawkes processes. Exploiting this connection renders a framework that can be built upon for expressive and flexible inference on diverse data. Specifically, multivariate unmarked Hawkes representations are introduced as a tool to parameterize univariate marked Hawkes processes. We show that such multivariate representations can asymptotically approximate a large class of univariate marked Hawkes processes, are stationary given the approximated process is stationary, and that resultant conditional intensity parameters are identifiable. A simulation study demonstrates the efficacy of this approach, and provides heuristic bounds for error induced by the relatively larger parameter space of multivariate Hawkes processes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
