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Superposition of interacting stochastic processes with memory and its application to migrating fish counts

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  • Yoshioka, Hidekazu

Abstract

Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as powerful tools in several research fields, including physics, mathematical economics, and environmental engineering. We formulate two novel mathematical models of long memory process based on a superposition of interacting processes driven by jumps. The mutual excitation among the processes to be superposed is assumed to be of the mean field or aggregation form, where the former yields a more analytically tractable model. The statistics of the proposed long memory processes are investigated using their moment-generating function, autocorrelation, and associated generalized Riccati equations. Finally, the proposed models are applied to time series data of migrating fish counts at river observation points. The results of this study suggest that an exponential memory or a long memory model is insufficient; however, a unified method that can cover both is necessary to analyze fish migration, and our model is exactly the case.

Suggested Citation

  • Yoshioka, Hidekazu, 2025. "Superposition of interacting stochastic processes with memory and its application to migrating fish counts," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924014632
    DOI: 10.1016/j.chaos.2024.115911
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    as
    1. Muir, Callum & Singh, Jaskeerat & Shah, Yawer & Bologna, Mauro & Grigolini, Paolo, 2024. "Influence of an environment changing in time on crucial events: From geophysics to biology," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    2. Abi Jaber, Eduardo & El Euch, Omar, 2019. "Markovian structure of the Volterra Heston model," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 63-72.
    3. Mouri, Goro & Shinoda, Seirou & Oki, Taikan, 2010. "Estimating Plecoglossus altivelis altivelis migration using a mass balance model expressed by hydrological distribution parameters in a major limpid river basin in Japan," Ecological Modelling, Elsevier, vol. 221(23), pages 2808-2815.
    4. Agathe-Nerine, Zoé, 2022. "Multivariate Hawkes processes on inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 86-148.
    5. Hottovy, Scott & Pagnini, Gianni, 2024. "Linear combinations of i.i.d. strictly stable variables with random coefficients and their application to anomalous diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 647(C).
    6. Wang, Jingyang & baoligao, Baiyin & Mu, Xiangpeng & Qie, Zhihong & Li, Guangning, 2024. "A coupled machine-learning-individual-based model for migration dynamics simulation: A case study of migratory fish in fish passage facilities," Ecological Modelling, Elsevier, vol. 498(C).
    7. Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03264893, HAL.
    8. Yoshioka, Hidekazu, 2024. "Modeling stationary, periodic, and long memory processes by superposed jump-driven processes," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    9. Hamaguchi, Yushi, 2024. "Markovian lifting and asymptotic log-Harnack inequality for stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    10. Kim, Jong-Ho & Park, Jea-Hyun, 2023. "Analysis of mono- and multi-cluster flocking for a nonlinear Cucker–Smale model with external force," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. Cox, Sonja & Karbach, Sven & Khedher, Asma, 2022. "Affine pure-jump processes on positive Hilbert–Schmidt operators," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 191-229.
    12. Yoshioka, Hidekazu & Yoshioka, Yumi, 2024. "Generalized divergences for statistical evaluation of uncertainty in long-memory processes," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    13. Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," LIDAM Reprints ISBA 2021014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    15. Danijel Grahovac & Nikolai N. Leonenko & Murad S. Taqqu, 2022. "Intermittency And Multiscaling In Limit Theorems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-18, November.
    16. Hainaut, Donatien, 2024. "A mutually exciting rough jump-diffusion for financial modelling," LIDAM Reprints ISBA 2024002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Marguet, Aline & Smadi, Charline, 2024. "Spread of parasites affecting death and division rates in a cell population," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    18. Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 120-132.
    19. Auconi, Andrea, 2024. "Interaction uncertainty in financial networks," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    20. Sahoo, Sushanta Kumar & Katlamudi, Madhusudhanarao & Pedapudi, Chandra Sekhar, 2024. "Multifractal detrended fluctuation analysis of soil radon in the Kachchh Region of Gujarat, India: A case study of earthquake precursors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    21. Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Post-Print hal-03264893, HAL.
    22. Christian Bayer & Simon Breneis, 2024. "Efficient option pricing in the rough Heston model using weak simulation schemes," Quantitative Finance, Taylor & Francis Journals, vol. 24(9), pages 1247-1261, September.
    23. Behme, Anita & Chong, Carsten & Klüppelberg, Claudia, 2015. "Superposition of COGARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1426-1469.
    24. Shen, Stanley W. & Tsai, Christina W., 2024. "Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    25. Zárate-Miñano, Rafael & Milano, Federico, 2016. "Construction of SDE-based wind speed models with exponentially decaying autocorrelation," Renewable Energy, Elsevier, vol. 94(C), pages 186-196.
    26. Finlay, Richard & Seneta, Eugene, 2012. "A Generalized Hyperbolic model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2164-2169.
    27. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    28. Cantisán, Julia & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2023. "Rotating cluster formations emerge in an ensemble of active particles," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    29. Lavallée, François & Smadi, Charline & Alvarez, Isabelle & Reineking, Björn & Martin, François-Marie & Dommanget, Fanny & Martin, Sophie, 2019. "A stochastic individual-based model for the growth of a stand of Japanese knotweed including mowing as a management technique," Ecological Modelling, Elsevier, vol. 413(C).
    30. Eduardo Abi Jaber & Omar El Euch, 2019. "Markovian structure of the Volterra Heston model," Post-Print hal-01716696, HAL.
    31. Rahvar, Sepehr & Reihani, Erfan S. & Golestani, Amirhossein N. & Hamounian, Abolfazl & Aghaei, Fatemeh & Sahimi, Muhammad & Manshour, Pouya & Paluš, Milan & Feudel, Ulrike & Freund, Jan A. & Lehnertz,, 2024. "Characterizing time-resolved stochasticity in non-stationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    32. Habyarimana, Cassien & Aduda, Jane A. & Scalas, Enrico & Chen, Jing & Hawkes, Alan G. & Polito, Federico, 2023. "A fractional Hawkes process II: Further characterization of the process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    33. Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," LIDAM Discussion Papers ISBA 2021019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    34. Olivares, Felipe & Sun, Xiaoqian & Wandelt, Sebastian & Zanin, Massimiliano, 2023. "Measuring landing independence and interactions using statistical physics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).
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