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Deconvolution of fractional brownian motion

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  • VLADAS PIPIRAS
  • MURAD S. TAQQU

Abstract

We show that a fractional Brownian motion with H′∈(0,1) can be represented as an explicit transformation of a fractional Brownian motion with index H ∈(0,1). In particular, when H′=½, we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion. We work both in the `time domain' and the `spectral domain' and contrast the advantages of one domain over the other.

Suggested Citation

  • Vladas Pipiras & Murad S. Taqqu, 2002. "Deconvolution of fractional brownian motion," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 487-501, July.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:4:p:487-501
    DOI: 10.1111/1467-9892.00274
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    Cited by:

    1. Harms, Philipp & Stefanovits, David, 2019. "Affine representations of fractional processes with applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1185-1228.
    2. Jost, Céline, 2006. "Transformation formulas for fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1341-1357, October.
    3. Davidson, James & Hashimzade, Nigar, 2009. "Representation And Weak Convergence Of Stochastic Integrals With Fractional Integrator Processes," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1589-1624, December.
    4. Biagini, Francesca & Fink, Holger & Klüppelberg, Claudia, 2013. "A fractional credit model with long range dependent default rate," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1319-1347.

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