000163626 001__ 163626
000163626 005__ 20181203022320.0
000163626 0247_ $$2doi$$a10.1137/090752638
000163626 02470 $$2ISI$$a000285509300004
000163626 037__ $$aARTICLE
000163626 245__ $$aFractional Brownian Vector Fields
000163626 269__ $$a2010
000163626 260__ $$bSIAM$$c2010
000163626 336__ $$aJournal Articles
000163626 520__ $$9eng$$aThis 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.
000163626 6531_ $$afractional Brownian motion
000163626 6531_ $$arandom vector fields
000163626 6531_ $$aself-similarity
000163626 6531_ $$ainvariance
000163626 6531_ $$aHelmholtz decomposition
000163626 6531_ $$ageneralized random processes
000163626 6531_ $$aGel'fand-Vilenkin stochastic analysis
000163626 6531_ $$aFractal Processes
000163626 6531_ $$aSelf-Similarity
000163626 6531_ $$aWavelets
000163626 6531_ $$aMotion
000163626 6531_ $$aRepresentation
000163626 6531_ $$aDecomposition
000163626 6531_ $$aDivergence
000163626 6531_ $$aTurbulence
000163626 6531_ $$aSplines
000163626 6531_ $$aModels
000163626 700__ $$aTafti, P.D.
000163626 700__ $$g115227$$aUnser, M.$$0240182
000163626 773__ $$j8$$tMultiscale Modeling & Simulation$$k5$$q1645–1670
000163626 8564_ $$uhttp://bigwww.epfl.ch/publications/tafti1003.html$$zURL
000163626 8564_ $$uhttp://bigwww.epfl.ch/publications/tafti1003.ps$$zURL
000163626 8564_ $$uhttps://infoscience.epfl.ch/record/163626/files/tafti1003.pdf$$zn/a$$s4308919
000163626 909C0 $$xU10347$$0252054$$pLIB
000163626 909CO $$ooai:infoscience.tind.io:163626$$pSTI$$pGLOBAL_SET$$particle
000163626 937__ $$aEPFL-ARTICLE-163626
000163626 970__ $$atafti1003/LIB
000163626 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000163626 980__ $$aARTICLE