当前位置: X-MOL 学术Stochastics › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Stochastic differential equations on fractal sets
Stochastics ( IF 0.9 ) Pub Date : 2019-12-03 , DOI: 10.1080/17442508.2019.1697268
Alireza K. Golmankhaneh 1 , Cemil Tunç 2
Affiliation  

ABSTRACT

In this manuscript, we review fractal calculus and random processes. Random variables and processes on totally disconnected fractal sets are defined. Random walks on fractal middle-ξ Cantor sets are suggested and corresponding variances are given which are power laws. The mean square stochastic calculus is generalized on fractal sets, which can lead to the standard case by setting dimension α = 1 . Furthermore, we solve a fractal stochastic differential equation using the Frobenius method. Graphs are presented to give more details.



中文翻译:

分形集上的随机微分方程

摘要

在本手稿中,我们回顾了分形演算和随机过程。定义了完全断开的分形集上的随机变量和过程。提出了在分形中间ξCantor集上的随机游动,并给出了相应的方差,它们是幂定律。均方随机演算是在分形集上推广的,通过设置维数可以得出标准情况 α = 1个 。此外,我们使用Frobenius方法求解分形随机微分方程。提供图形以提供更多详细信息。

更新日期:2019-12-03
down
wechat
bug