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Asymptotic Properties and Application of GSB Process: A Case Study of the COVID-19 Dynamics in Serbia

Author

Listed:
  • Mihailo Jovanović

    (The Office for Information Technologies and eGovernment, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Vladica Stojanović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Kristijan Kuk

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Brankica Popović

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Petar Čisar

    (Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

Abstract

This paper describes one of the non-linear (and non-stationary) stochastic models, the GSB (Gaussian, or Generalized, Split-BREAK) process, which is used in the analysis of time series with pronounced and accentuated fluctuations. In the beginning, the stochastic structure of the GSB process and its important distributional and asymptotic properties are given. To that end, a method based on characteristic functions (CFs) was used. Various procedures for the estimation of model parameters, asymptotic properties, and numerical simulations of the obtained estimators are also investigated. Finally, as an illustration of the practical application of the GSB process, an analysis is presented of the dynamics and stochastic distribution of the infected and immunized population in relation to the disease COVID-19 in the territory of the Republic of Serbia.

Suggested Citation

  • Mihailo Jovanović & Vladica Stojanović & Kristijan Kuk & Brankica Popović & Petar Čisar, 2022. "Asymptotic Properties and Application of GSB Process: A Case Study of the COVID-19 Dynamics in Serbia," Mathematics, MDPI, vol. 10(20), pages 1-28, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3849-:d:945153
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    References listed on IDEAS

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    Cited by:

    1. Alexander N. Tikhomirov & Vladimir V. Ulyanov, 2023. "On the Special Issue “Limit Theorems of Probability Theory”," Mathematics, MDPI, vol. 11(17), pages 1-4, August.

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