An extension of stochastic differential models by using the Grunwald-Letnikov fractional derivative
Publish place: Theory of Approximation and Applications، Vol: 16، Issue: 1
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_MSJI-16-1_002
تاریخ نمایه سازی: 17 بهمن 1401
Abstract:
Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach based on least square approximation is applied to determine the order of the fractional derivative. Numerical examples show that the proposed model works better than the SDE to model stochastic processes with memory.
Keywords:
fractional derivative , Grunwald-Letnikov fractional derivative , Stochastic differential model , Stochastic process with memory
Authors
Mohammad Ali Jafari
Department of Financial Sciences, Kharazmi University, P.O. Box ۱۵۸۷۵-۱۱۱۱, Tehran, Iran.
Narges Mousaviy
Department of Financial Sciences, Kharazmi University, P.O. Box ۱۵۸۷۵-۱۱۱۱, Tehran, Iran.