Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant periods. The lengths of the constant periods follow a one-sided distribution which involves a parameter between 0 and 1 and whose first moment does not exist. This paper constructs an estimator for the parameter, applying the method of moments to the number of observed constant periods in a fixed time interval. The resulting estimator is asymptotically unbiased and consistent, and it is well-suited for situations where multiple observations of the same subdiffusion process are available. We present supporting numerical examples and an application to market price data for a low-volume stock.

中文翻译：

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单边重尾分布的参数估计

稳定的从属子以及具有幂律概率尾的更一般的从属子，已广泛用于子扩散的上下文中，其中粒子在多个时间段内被捕获或固定，称为恒定周期。恒定周期的长度遵循单边分布，该分布涉及一个介于 0 和 1 之间的参数，并且其一阶矩不存在。本文构造了参数的估计量，将矩法应用于固定时间间隔内观察到的恒定周期数。由此产生的估计量是渐近无偏和一致的，它非常适用于同一子扩散过程的多个观察可用的情况。我们提供了支持性的数值示例以及对小批量股票的市场价格数据的应用。