Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables

被引：27

作者：

Di Paola, Mario ^{[1
]}

Pinnola, Francesco Paolo ^{[1
]}

机构：

[1] Univ Palermo, Dipartimento Ingn Civile Ambientale & Aerospazial, I-90128 Palermo, Italy

来源：

PROBABILISTIC ENGINEERING MECHANICS | 2012年 / 29卷

关键词：

Fractional calculus; Mellin transform; Complex order moments; Fractional moments; Fractional spectral moments; Probability density function; Characteristic function; CALCULUS;

D O I：

10.1016/j.probengmech.2011.11.003

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an alpha-stable random variable is discussed in detail, showing the impressive capability to characterize random variables in terms of fractional moments. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：149 / 156

页数：8

共 50 条

[1] On fractional moments of random variables
Boyarinov, R. N.
[J]. DOKLADY MATHEMATICS, 2011, 83 (01) : 53 - 55
[2] On fractional moments of random variables
R. N. Boyarinov
[J]. Doklady Mathematics, 2011, 83 : 53 - 55
[3] On the use of fractional calculus for the probabilistic characterization of random variables
Cottone, Giulio
Di Paola, Mario
[J]. PROBABILISTIC ENGINEERING MECHANICS, 2009, 24 (03) : 321 - 330
[4] An improved complex fractional moment-based approach for the probabilistic characterization of random variables
Dai, Hongzhe
Ma, Zixuan
Li, Liang
[J]. PROBABILISTIC ENGINEERING MECHANICS, 2018, 53 : 52 - 58
[5] Fractional characteristic functions, and a fractional calculus approach for moments of random variables
Tomovski, Zivorad
Metzler, Ralf
Gerhold, Stefan
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2022, 25 (04) : 1307 - 1323
[6] Fractional characteristic functions, and a fractional calculus approach for moments of random variables
Živorad Tomovski
Ralf Metzler
Stefan Gerhold
[J]. Fractional Calculus and Applied Analysis, 2022, 25 : 1307 - 1323
[7] DISTRIBUTIONAL FRACTIONAL-POWERS AND RIESZ FRACTIONAL INTEGRALS
SCHIAVONE, SE
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 165 (02) : 565 - 574
[8] FRACTIONAL-POWERS OF OPERATORS AND RIESZ FRACTIONAL INTEGRALS
SCHIAVONE, SE
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1989, 112 : 237 - 247
[9] RIESZ AND VALIRON MEANS AND FRACTIONAL MOMENTS
BINGHAM, NH
TENENBAUM, G
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1986, 99 : 143 - 149
[10] Random variables as pathwise integrals with respect to fractional Brownian motion
Mishura, Yuliya
Shevchenko, Georgiy
Valkeila, Esko
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (06) : 2353 - 2369

← 1 2 3 4 5 →