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Wavelets and stochastic processes


  • Antoniou, I.
  • Gustafson, K.


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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    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. 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.
    3. repec:eee:finmar:v:37:y:2018:i:c:p:97-119 is not listed on IDEAS
    4. 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.
    5. 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.
    6. 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.
    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, 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.


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