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Deconvolution of fractional brownian motion
Author(s) -
PIPIRAS VLADAS,
TAQQU MURAD S.
Publication year - 2002
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00274
Subject(s) - fractional brownian motion , mathematics , brownian motion , reflected brownian motion , brownian excursion , domain (mathematical analysis) , deconvolution , mathematical analysis , fractional calculus , representation (politics) , autoregressive model , martingale representation theorem , geometric brownian motion , diffusion process , statistics , knowledge management , innovation diffusion , politics , computer science , political science , law
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.