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

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.

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Year of publication:	2007
Authors:	van Zanten, Harry
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 117.2007, 1, p. 57-70
Publisher:	Elsevier
Keywords:	Equivalence Fractional Brownian motion Frequency domain Reproducing kernels Stationary increments

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008872703