Stochastic Processes and Mean Square Calculus on Fractal Curves

2023/10/21 by Alireza Khalili Golmankhaneh, Golmankhaneh, Alireza Khalili, Kerri Welch +5
Computer Science · Mathematics · #28A80 #60G12 #60G18 #60G20 #60H05 #Computational Physics and Python Applications #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.09648

openalex publication_date 2023/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define cumulative distribution function, probability density function, moments, variance and correlation function of stochastic process on fractal curve. A new framework which is a generalization of mean square calculus is formulated. Sequence of random variable on fractal curve, fractal mean square continuity, mean square F^α-derivative, and fractal mean square integral. The mean square solution of a fractal stochastic equation is derived and plotted in order to show the details.

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