When is a linear combination of independent fBm's equivalent to a single fBm?

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Abstract

We study and answer the question posed in the title. The answer is derived from some new necessary and sufficient conditions for equivalence of Gaussian processes with stationary increments and recent frequency domain results for the fBm. The result shows in particular precisely in which cases the local almost sure behaviour of a linear combination of independent fBm's is the same as that of a multiple of a single fBm. © 2006 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)57-70
JournalStochastic Processes and Their Applications
Volume117
Issue number1
DOIs
Publication statusPublished - 2007

Bibliographical note

MR2287103

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