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Fractional Stochastic Search Algorithms: Modelling Complex Systems via AI

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  • Bodo Herzog

    (Economic & Data Science Department, ESB Business School, Reutlingen University, Alteburgstr. 150, 72762 Reutlingen, Germany
    RRI-Reutlingen Research Institute, Reutlingen University, 72762 Reutlingen, Germany)

Abstract

The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes { B t H , t ≥ 0 } with the Hurst parameter H ∈ ( 0 , 1 ) . We define and discuss the properties of fractional stochastic processes, { B t H , t ≥ 0 } , which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.

Suggested Citation

  • Bodo Herzog, 2023. "Fractional Stochastic Search Algorithms: Modelling Complex Systems via AI," Mathematics, MDPI, vol. 11(9), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2061-:d:1133822
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    References listed on IDEAS

    as
    1. Bodo Herzog, 2022. "Adopting Feynman–Kac Formula in Stochastic Differential Equations with (Sub-)Fractional Brownian Motion," Mathematics, MDPI, vol. 10(3), pages 1-13, January.
    2. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    3. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
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