英文标题：
《Hybrid marked point processes: characterisation, existence and
uniqueness》
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作者：
Maxime Morariu-Patrichi, Mikko S. Pakkanen
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最新提交年份：
2018
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英文摘要：
We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and are endowed with a state process that interacts with past-dependent events. The key example we entertain is an extension of a Hawkes process, a state-dependent Hawkes process interacting with its state process. We show the existence and uniqueness of hybrid marked point processes under general assumptions, extending the results of Massouli\\\'e (1998) on interacting point processes.
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中文摘要：
我们引入了一类混合标记点过程，它包含并扩展了连续时间马尔可夫链和霍克斯过程。虽然这个灵活的类合并了这些现有流程，但它还包含具有复杂动力学的新流程。这些过程是通过其强度隐式定义的，并被赋予一个与过去相关事件交互的状态过程。我们考虑的关键例子是霍克斯过程的扩展，一个状态相关的霍克斯过程与其状态过程相互作用。在一般假设下，我们证明了混合标记点过程的存在性和唯一性，推广了Massouli \\（1998）关于相互作用点过程的结果。
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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
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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