Fractional Brownian motion (fBm) is an important mathematical model for describing a range of phenomena and processes. The properties of discrete time fBm (dfBm) when m equals 1 and 2 have been reported in the literature. This paper focuses on analysis of auto-covariance matrix of the m-th order (m > 2) of a dfBm process and the error associated with the approximation of a large dimensional auto-covariance matrix. Applying matrix theory and analysis, we also generalize the asymptotic properties of the eigenvalues of the auto-covariance matrix. Based on the analysis, two theorems and one lemma are proposed and their proofs are provided.
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|Title of host publication||Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering|
|Subtitle of host publication||Halifax, Canada, May 3-6, 2015|
|Place of Publication||Piscataway, NJ|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||5|
|Publication status||Published - 2015|
|Event||Canadian Conference on Electrical and Computer Engineering (28th : 2015) - Halifax, Canada|
Duration: 3 May 2015 → 6 May 2015
Conference number: 28th
|Conference||Canadian Conference on Electrical and Computer Engineering (28th : 2015)|
|Period||3/05/15 → 6/05/15|