3 papers
math.PR2007
Stationarity and Self-similarity Characterization of the Set-indexed Fractional Brownian Motion
Erick Herbin, Ely Merzbach
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 pr…
math.PR2005
From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions
E. Herbin
Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the Holder regularity is allowed to vary along the paths. In this paper, two kind…
math.PR2005
A set-indexed fractional Brownian motion
E. Herbin, E. Merzbach
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed…