Densities of Scaling Limits of Coupled Continuous Time Random Walks

被引：0
作者：
Marcin Magdziarz
Tomasz Zorawik
机构：
[1] University of Science and Technology,Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wroclaw
来源：
Fractional Calculus and Applied Analysis | 2016年 / 19卷
关键词：
Primary 26A33; Secondary 60G52; 60E07; Lévy walk; fractional material derivative; Meijer ; function; fractional differential equation; α-stable distribution; Lévy process;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer G-function. This allows to efficiently evaluate them numerically. We also compute two-point distribution of wait-first model. Our results show perfect agreement with the Monte Carlo simulations.
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页码：1488 / 1506
页数：18
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