On the linear structure of self-similar processes

Carl J. Nuzman; H. Vincent Poor

doi:10.1109/ISIT.2000.866796

On the linear structure of self-similar processes

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	498
Number of pages	1
Journal	IEEE International Symposium on Information Theory - Proceedings
DOIs	https://doi.org/10.1109/ISIT.2000.866796
State	Published - 2000

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2000.866796

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title = "On the linear structure of self-similar processes",

abstract = "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.",

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AB - 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.

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On the linear structure of self-similar processes

Abstract

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