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A Fractional Process with Jumps for Modeling Karstic Spring Discharge Data

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  • Dániel Boros

    (Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
    Doctoral School of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary)

  • Edit Borbás

    (Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary)

  • Amina Darougi

    (Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
    Doctoral School of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary)

  • József Kovács

    (Department of Physical and Applied Geology, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary)

  • László Márkus

    (Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
    Doctoral School of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary)

Abstract

Fractal dimensions for the daily discharge data series of several karstic springs in northeast Hungary have recently been computed and analyzed. We model four of those series with similar fractal dimensions using a superposition of a fractional Ornstein–Uhlenbeck process and a jump process of renewal–reward type. Beyond some usual goodness-of-fit measures, simulations of the model show an visually appealing good fit. When the fractal dimension is not taken into account in the modeling, the simulated accumulated discharges tend to significantly exceed realistic values.

Suggested Citation

  • Dániel Boros & Edit Borbás & Amina Darougi & József Kovács & László Márkus, 2025. "A Fractional Process with Jumps for Modeling Karstic Spring Discharge Data," Mathematics, MDPI, vol. 13(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2928-:d:1746126
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