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Wavelets and stochastic processes

Author

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  • Antoniou, I.
  • Gustafson, K.

Abstract

Wavelets are known to have intimate connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, and filter banks. Here, we establish and survey a new connection, namely to stochastic processes. Key to this link are the Kolmogorov systems of ergodic theory.

Suggested Citation

  • Antoniou, I. & Gustafson, K., 1999. "Wavelets and stochastic processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 81-104.
    • Handle: RePEc:eee:matcom:v:49:y:1999:i:1:p:81-104
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    Citations

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    Cited by:

    1. Levan, N. & Kubrusly, C.S., 2003. "A wavelet “time-shift-detail” decomposition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(2), pages 73-78.
    2. Pham, Joseph N.Q., 2000. "A unilateral shift setting for the fast wavelet transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(5), pages 361-379.
    3. Kubrusly, Carlos S. & Levan, Nhan, 2004. "Shift reducing subspaces and irreducible-invariant subspaces generated by wandering vectors and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(6), pages 607-627.
    4. Jozef Barunik & Lukas Vacha, 2015. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1347-1364, August.
    5. Barunik, Jozef & Krehlik, Tomas & Vacha, Lukas, 2016. "Modeling and forecasting exchange rate volatility in time-frequency domain," European Journal of Operational Research, Elsevier, vol. 251(1), pages 329-340.
    6. Miloš Milovanović & Srđan Vukmirović & Nicoletta Saulig, 2021. "Stochastic Analysis of the Time Continuum," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    7. Barunik, Jozef & Vacha, Lukas, 2018. "Do co-jumps impact correlations in currency markets?," Journal of Financial Markets, Elsevier, vol. 37(C), pages 97-119.
    8. Gialampoukidis, I. & Gustafson, K. & Antoniou, I., 2014. "Time operator of Markov chains and mixing times. Applications to financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 141-155.
    9. Miloš Milovanović & Nicoletta Saulig, 2024. "The Duality of Psychological and Intrinsic Time in Artworks," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    10. 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.
    11. Gialampoukidis, Ilias & Antoniou, Ioannis, 2015. "Age, Innovations and Time Operator of Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 140-155.
    12. Miloš Milovanović, 2023. "The Measurement Problem in Statistical Signal Processing," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    13. Gialampoukidis, I. & Gustafson, K. & Antoniou, I., 2013. "Financial Time Operator for random walk markets," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 62-72.

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