This study considers a new multi-term urn process that has a correlation in the same term and temporal correlation. The objective is to clarify the relationship between the urn model and the Hawkes process. Correlation in the same term is represented by the P\'{o}lya urn model and the temporal correlation is incorporated by introducing the conditional initial condition. In the double-scaling limit of this urn process, the self-exciting negative binomial distribution (SE-NBD) process, which is a marked point process, is obtained. In the standard continuous limit, this process becomes the Hawkes process, which has no correlation in the same term. The difference is the variance of the intensity function in that the phase transition from the steady to the non-steady state can be observed. The critical point, at which the power law distribution is obtained, is the same for the Hawkes and the urn processes. These two processes are used to analyze empirical data of financial default to estimate the parameters of the model. For the default portfolio, the results produced by the urn process are superior to those obtained with the Hawkes process and confirm self-excitation.

翻译：本研究将考虑一个新的多周期内分泌过程,该过程在同一个术语和时间关系中具有相关性。 目的是澄清内脏模型和霍克斯过程之间的关系。 同一术语的关联由 P\' {o}lya URn 模型和时间相关性组成, 引入有条件初始条件。 在这个内脏过程的双缩放限制中, 获得自我激发的负二进制分布( SE- NBD) 进程, 这是一个标志性点进程。 在标准连续限制中, 这一过程成为霍克斯 进程, 在同一术语中没有关联性。 区别在于从稳定状态向非稳定状态的阶段过渡的强度函数差异。 获得权力法分布的临界点与霍克斯 和 urn 进程相同。 这两个过程用来分析财务违约的经验数据, 以估计模型的参数。 在默认组合中, 内脏过程产生的结果优于与霍克斯 进程和自我验证的结果。