On the linear structure of self-similar processes

Carl J. Nuzman, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review


Self-similar processes have a rich linear structure, based on scale invariance, which is analogous to the shift-invariant structure of stationary processes. The analogy is made explicit via Lamperti's perti's transformation. This transformation is used here to characterize the reproducing kernel Hilbert space (RKHS) associated with self-similar processes and hence to solve problems of prediction, whitening, and Gaussian signal detection. Some specific results for the fractional Brownian motion illustrate the general concepts.

Original languageEnglish (US)
Pages (from-to)498
Number of pages1
JournalIEEE International Symposium on Information Theory - Proceedings
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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