The main contribution of the paper amounts to providing a mathematical construction of a generalized multivariate Hawkes process (GMHP), as well as a simulation algorithm based on this construction. In particular, we justify the construction by demonstrating that the constructed process is indeed a GMHP with desired properties. Towards this end we provide some new results regarding conditional Poisson random measures and doubly stochastic marked Poisson processes.

中文翻译：

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广义多元霍克斯过程的构建与仿真

该论文的主要贡献在于提供了广义多元霍克斯过程 (GMHP) 的数学构造，以及基于该构造的模拟算法。特别是，我们通过证明构造过程确实是具有所需特性的 GMHP 来证明构造的合理性。为此，我们提供了一些关于条件泊松随机测量和双随机标记泊松过程的新结果。