广义Mittag-Leffler分布和过程在天体物理学和时间序列建模中的应用
Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling
摘要：
引入了具有Laplace变换的几何广义Mittag-Leffler分布$\frac{1}{1+β\log(1+t^α)},0<α\le 2,β>0$，并讨论了它的性质.建立了Mittag-Leffler边际分布和几何广义Mittag-Leffler边际分布的自回归过程。Haubold和Mathai（2000）导出了分数动力学方程和热核函数在Mittag-Leffler函数下的封闭形式表示。Saxena等人（2002，2004 a，b）推广了这一结果，得到了一些分数阶动力学方程的广义Mittag-Leffler函数解。这些结果有助于解释物理学的各种基本定律。在这里，我们开发了一阶自回归时间序列模型和属性进行了探讨。其结果在天体物理学、空间科学、气象学、金融建模和可靠性建模等各个领域都有应用。
英文摘要：
Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+β\log(1+t^α)},0<α\le 2,β>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.
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