Mellin transform for the probabilistic characterization of random variables and stochastic processes

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI:10.1016/j.probengmech.2025.103766

S. Russotto , A. Pirrotta

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引用次数: 0

Abstract

The probabilistic characterization of random variables and stochastic processes involves the evaluation of the probability density function or characteristic function. The latter is typically obtained by using integer-order statistical moments, that could lead to divergence problem for high-order moments especially in case of heavy-tailed distributions, such as the distribution of the α-stable random variables. On the other hand, recent approaches that use complex fractional moments, offer a more robust probabilistic description, but for particular cases.

In this paper, a novel approach based on Mellin transform for the probabilistic characterization of random variables is proposed. Starting from numerical data, this approach is effective for the evaluation of both the probability density function and the characteristic function, and then is valid for a wide class of random variables. Further, an extension of the approach from random variables to stochastic processes is proposed. The reliability of the proposed approach is assessed through several numerical simulations involving α-stable distributions, Gaussian distributions and α-stable stochastic processes.

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Mellin变换用于随机变量和随机过程的概率表征

随机变量和随机过程的概率表征涉及概率密度函数或特征函数的评估。后者通常由整阶统计矩获得，这可能导致高阶矩的散度问题，特别是在重尾分布的情况下，例如α-稳定随机变量的分布。另一方面，最近使用复杂分数矩的方法提供了更健壮的概率描述，但仅限于特定情况。本文提出了一种基于Mellin变换的随机变量概率表征方法。从数值数据出发，该方法对概率密度函数和特征函数的求值都是有效的，进而对广泛的随机变量类都是有效的。进一步，提出了一种从随机变量到随机过程的扩展方法。通过α-稳定分布、高斯分布和α-稳定随机过程的数值模拟，验证了该方法的可靠性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Probabilistic Engineering Mechanics 工程技术-工程：机械

CiteScore

3.80

自引率

15.40%

发文量

审稿时长

13.5 months

期刊介绍： This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.