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Stochastic Analysis of the Time Continuum

Author

Listed:
  • Miloš Milovanović

    (Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia)

  • Srđan Vukmirović

    (Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia)

  • Nicoletta Saulig

    (Faculty of Engineering, Juraj Dobrila University of Pula, 52100 Pula, Croatia)

Abstract

This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics.

Suggested Citation

  • Miloš Milovanović & Srđan Vukmirović & Nicoletta Saulig, 2021. "Stochastic Analysis of the Time Continuum," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1452-:d:578889
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    References listed on IDEAS

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    1. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    2. Antoniou, I. & Gustafson, K., 1999. "Wavelets and stochastic processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 81-104.
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    Cited by:

    1. Miloš Milovanović & Nicoletta Saulig, 2022. "An Intensional Probability Theory: Investigating the Link between Classical and Quantum Probabilities," Mathematics, MDPI, vol. 10(22), pages 1-16, November.

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