标题： 一种用于建模最大跑步期间心率序列的新随机过程及其分形参数的估计器 显示英文标题

标题： A new stochastic process to model Heart Rate series during exhaustive run and an estimator of its fractality parameter

摘要： 为了解释和说明生理信号行为，找出这些数据在所有努力期间或在比赛的不同阶段的波动中的某些常数可能是有趣的（可以使用变化点检测方法来检测这些常数）。 最近几篇论文提出了长程依赖（Hurst）参数作为这样的常数。 然而，它们的结果引发了两个主要问题。 首先，DFA方法通常用于估计这个参数。显然，这种方法并不能提供最有效的估计量，而且即使在平滑趋势的情况下，它也不是完全稳健的。 其次，这种方法经常给出大于1的估计Hurst参数，而这是长记忆平稳过程的最大可能值。 在本文中，我们为这两个问题提出了解决方案，并定义了一个允许这种估计参数的新模型。 显示英文摘要

摘要： In order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected using a change points detection method). Several recent papers have proposed the long-range dependence (Hurst) parameter as such a constant. However, their results induce two main problems. Firstly, DFA method is usually applied for estimating this parameter. Clearly, such a method does not provide the most efficient estimator and moreover it is not at all robust even in the case of smooth trends. Secondly, this method often gives estimated Hurst parameters larger than 1, which is the larger possible value for long memory stationary processes. In this article we propose solutions for both these problems and we define a new model allowing such estimated parameters.