Abstract

In this paper, we present the results of applying the model of cyclic point processes with a limited aftereffect for the analysis of the rhythmic characteristics of pulsed signals. Being a generalization of recurrent and alternating point processes, we show that cyclic processes can describe event flows with more than two states. The latter circumstance significantly expands the scope of their application, in particular, to biomedical signals. Here, a complete (local) statistical description of the cyclic processes is derived, the asymptotics of their behavior are studied, and a simplified statistical description for the case of stationary modes is given. In the latter case, analytical expressions for the average and second mixed moments of the cyclic process are obtained based on the local statistics. In the most important particular case, the dependence of the features of their structure on the time scales of the signal dynamics and on the ratios between the scales was clarified.

中文翻译：

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具有显着脉搏变异性的脉冲信号分析的后效应有限的循环点过程

摘要

在本文中，我们介绍了将循环点过程模型具有有限后效应的结果用于分析脉冲信号的节奏特性。作为循环和交替点过程的概括，我们证明循环过程可以描述具有两个以上状态的事件流。后一种情况极大地扩展了它们的应用范围，尤其是在生物医学信号方面。在这里，获得了一个完整的（局部）循环过程的统计描述，研究了它们的行为的渐近性，并给出了平稳模式情况下的简化统计描述。在后一种情况下，基于局部统计量获得循环过程的平均和第二混合矩的解析表达式。在最重要的特殊情况下，