A Fractional Process with Jumps for Modeling Karstic Spring Discharge Data

Dániel Boros, Edit Borbás, Amina Darougi, József Kovács and László Márkus ()
Additional contact information
Dániel Boros: Department of Probability Theory and Statistics, 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
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

Mathematics, 2025, vol. 13, issue 18, 1-24

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.

Keywords: fractal dimension; karstic aquifer; fractional Ornstein–Uhlenbeck process; jump process; renewal–reward process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/2928/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/2928/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:18:p:2928-:d:1746126

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().