Stochastic processes and mean square calculus on fractal curves

Khalili Golmankhaneh A., Welch K., Serpa C., Stamova I.

Random Operators and Stochastic Equations, cilt.32, sa.3, ss.211-222, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/rose-2024-2009
  • Dergi Adı: Random Operators and Stochastic Equations
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.211-222
  • Anahtar Kelimeler: fractal curve, fractal stochastic equation, mean square calculus
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define the cumulative distribution function, probability density function, moments, variance, and correlation function of stochastic processes on fractal curves. A new framework, which is a generalization of mean square calculus, is formulated. The sequence of random variables on the fractal curve, fractal mean square continuity, mean square F α {F^{\alpha}} -derivative, and fractal mean square integral are discussed. The mean square solution of a fractal stochastic equation is derived and plotted to illustrate the details.