Multifractional processes with random exponent

Multifractional processes with random exponent

Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet serie...

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Veröffentlicht in:Publicacions matemàtiques 2005, Vol.49 (2), p.459-486
Hauptverfasser: Ayache, A., Taqqu, M. S.
Format: Artikel
Sprache:eng
Schlagworte:
Brownian motion
Fourier transformations
Integers
Mathematical functions
Mathematical integrals
Random variables
Series convergence
Stochastic processes
Trajectories
White noise
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Zusammenfassung:Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Hölder regularity and their self-similarity.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_49205_11