English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The set-indexed fractional Brownian motion (sifBm) has been defined byHerbin-Merzbach (2006) for indices that are subsets of a metric measure space.In this paper, the sifBm is proved to statisfy a strenghtened definition ofincrement stationarity. This new definition for stationarity property allows toget a complete characterization of this process by its fractal properties: ThesifBm is the only set-indexed Gaussian process which is self-similar and hasstationary increments.  Using the fact that the sifBm is the only set-indexed process whoseprojection on any increasing path is a one-dimensional fractional Brownianmotion, the limitation of its definition for a self-similarity parameter0<H<1/2 is studied, as illustrated by some examples. When the indexingcollection is totally ordered, the sifBm can be defined for 0<H<1.

Stationarity and Self-similarity Characterization of the Set-indexed Fractional Brownian Motion