| Autor: |
Herbin, Erick, Merzbach, Ely |
| Rok vydání: |
2007 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin-Merzbach (2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is proved to statisfy a strenghtened definition of increment stationarity. This new definition for stationarity property allows to get a complete characterization of this process by its fractal properties: The sifBm is the only set-indexed Gaussian process which is self-similar and has stationary increments. Using the fact that the sifBm is the only set-indexed process whose projection on any increasing path is a one-dimensional fractional Brownian motion, the limitation of its definition for a self-similarity parameter 0Comment: 18 pages |
| Databáze: |
arXiv |
| Externí odkaz: |
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