Stochastic differential equations on fractal sets


Golmankhaneh A. K. , TUNÇ C.

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası:
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/17442508.2019.1697268
  • Dergi Adı: STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES

Özet

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-xi 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 . Furthermore, we solve a fractal stochastic differential equation using the Frobenius method. Graphs are presented to give more details.