DENSITIES OF SCALING LIMITS OF COUPLED CONTINUOUS TIME RANDOM WALKS

被引：7
|
作者：
Magdziarz, Marcin [1 ]
Zorawik, Tomasz [1 ]
机构：
[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Hugo Steinhaus Ctr, Wyspianskiego 27, PL-50370 Wroclaw, Poland
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 06期
关键词：
Levy walk; fractional material derivative; Meijer G function; fractional differential equation; alpha-stable distribution; Levy process; LEVY WALKS; THEOREMS;
D O I：
10.1515/fca-2016-0077
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we derive explicit formulas for the densities of Levy 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.
引用
收藏
页码：1488 / 1506
页数：19
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