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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation
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Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

机译：具有添加剂随机噪声的过滤泊松过程的统计特性：分布，相关性和矩估计

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摘要

Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the. power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.
机译：过滤的泊松过程通常用作物理系统中间歇波动的参考模型。这里通过将噪声术语添加到过程中的纯附加术语或作为随机微分方程中的动态术语来延伸这种过程。导出最低阶矩，概率密度函数，自相关函数和功率谱密度，用于识别和比较两种不同噪声术语的效果。合成时间序列的Monte-Carlo研究用于研究模型参数估计的准确性，并识别区分噪声类型的方法。结果表明，概率密度函数和三个最低阶矩提供了模型参数的准确估计，但无法分离噪声类型。自相关函数和。功率谱密度还提供用于估计模型参数的方法，以及能够识别噪声类型。信号在正方向上交叉规定的阈值水平的次数也有望能够区分噪声类型。

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