Linear estimation of self-similar processes via Lamperti's transformation

Carl J. Nuzman, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Lamperti's transformation, an isometry between self-similar and stationary processes, is used to solve some problems of linear estimation of continuous-time, self-similar processes. These problems include causal whitening and innovations representations on the positive real line, as well as prediction from certain finite and semi-infinite intervals. The method is applied to the specific case of fractional Brownian motion (FBM), yielding alternate derivations of known prediction results, along with some novel whitening and interpolation formulae. Some associated insights into the problem of discrete prediction are also explored. Closed-form expressions for the spectra and spectral factorization of the stationary processes associated with the FBM are obtained as part of this development.

Original languageEnglish (US)
Pages (from-to)429-452
Number of pages24
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


  • Fractional Brownian motion
  • Innovations
  • Lamperti's transformation
  • Linear prediction
  • Scale-stationary processes
  • Self-similar processes
  • Whitening
  • Wiener-Kolmogorov filter


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