TY - EJOUR
DO - 10.1137/090752638
AB - This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical invariances of standard vector fBm (self-similarity and rotation invariance) but which, in contrast, have dependent vector components in the general case. These random vector fields result from the transformation of white noise by a special operator whose invariance properties the random field inherits. The said operator combines an inverse fractional Laplacian with a Helmholtz-like decomposition and weighted recombination. Classical fBm's can be obtained by balancing the weights of the Helmholtz components. The introduced random fields exhibit several important properties that are discussed in this paper. In addition, the proposed scheme yields a natural extension of the definition to Hurst exponents greater than one.
T1 - Fractional Brownian Vector Fields
IS - 5
DA - 2010
AU - Tafti, P.D.
AU - Unser, M.
JF - Multiscale Modeling & Simulation
SP - 1645–1670
VL - 8
EP - 1645–1670
PB - SIAM
ID - 163626
KW - fractional Brownian motion
KW - random vector fields
KW - self-similarity
KW - invariance
KW - Helmholtz decomposition
KW - generalized random processes
KW - Gel'fand-Vilenkin stochastic analysis
KW - Fractal Processes
KW - Self-Similarity
KW - Wavelets
KW - Motion
KW - Representation
KW - Decomposition
KW - Divergence
KW - Turbulence
KW - Splines
KW - Models
UR - http://bigwww.epfl.ch/publications/tafti1003.html
UR - http://bigwww.epfl.ch/publications/tafti1003.ps
UR - http://infoscience.epfl.ch/record/163626/files/tafti1003.pdf
ER -