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Volumn 15, Issue 1, 2007, Pages 73-87

Definition, properties and wavelet analysis of multiscale fractional brownian motion

Author keywords

Fractional Brownian motion; Functional central limit theorem; Long range dependence; Path regularity; Self similarity; Wavelet analysis

Indexed keywords

BIOMECHANICS; BROWNIAN MOVEMENT; TELECOMMUNICATION TRAFFIC; THEOREM PROVING; TURBULENCE;

EID: 34147112303     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X07003356     Document Type: Article
Times cited : (16)

References (29)
  • 1
    • 0000501589 scopus 로고
    • Fractional Brownian motion, fractional noises and applications
    • B. Mandelbrot and J. Van Ness, Fractional Brownian motion, fractional noises and applications, SIAM Rev. 10 (1968) 422-437.
    • (1968) SIAM Rev , vol.10 , pp. 422-437
    • Mandelbrot, B.1    Van Ness, J.2
  • 3
    • 0003879309 scopus 로고    scopus 로고
    • Multifractional Brownian Motion: Definition and Preliminary Results
    • INRIA
    • R. Peltier and J. Lévy Véhel, Multifractional Brownian Motion: Definition and Preliminary Results (Rapport Technique INRIA, 1996).
    • (1996) Rapport Technique
    • Peltier, R.1    Lévy Véhel, J.2
  • 4
    • 0031496443 scopus 로고    scopus 로고
    • Elliptic Gaussian random processes
    • A. Benassi, S. Jaffard and D. Roux, Elliptic Gaussian random processes, Rev. Math. Iberoam. 13(1) (1997) 19-90.
    • (1997) Rev. Math. Iberoam , vol.13 , Issue.1 , pp. 19-90
    • Benassi, A.1    Jaffard, S.2    Roux, D.3
  • 6
    • 1642549817 scopus 로고    scopus 로고
    • Identification of the Hurst index of a step fractional Brownian motion
    • A. Benassi, P. Bertrand, S. Cohen and J. Istas, Identification of the Hurst index of a step fractional Brownian motion, Stat. Inference Stochastic Process. 3(1/2) (2000) 101-111.
    • (2000) Stat. Inference Stochastic Process , vol.3 , Issue.1-2 , pp. 101-111
    • Benassi, A.1    Bertrand, P.2    Cohen, S.3    Istas, J.4
  • 7
    • 33749515596 scopus 로고    scopus 로고
    • A central limit theorem for the generalized quadratic variations of the step fractional Brownian motion, to appear in Stat. Inference Stochastic
    • A. Ayache, P. Bertrand and J. Lévy Véhel, A central limit theorem for the generalized quadratic variations of the step fractional Brownian motion, to appear in Stat. Inference Stochastic Process. 10 (2007) 1-27.
    • (2007) Process , vol.10 , pp. 1-27
    • Ayache, A.1    Bertrand, P.2    Lévy Véhel, J.3
  • 8
    • 4544260770 scopus 로고    scopus 로고
    • Stable stationary processes related to cyclic flows
    • 3A, 2222-2260
    • V. Pipiras and M. S. Taqqu, Stable stationary processes related to cyclic flows, Ann. Prob. 23(3A) (2004) 2222-2260.
    • (2004) Ann. Prob , vol.23
    • Pipiras, V.1    Taqqu, M.S.2
  • 11
    • 0345276870 scopus 로고    scopus 로고
    • Wavelet based estimation of local Kolmogorov turbulence
    • eds. P. Doukhan, G. Oppenheim and M. S. Taqqu Birkhäuser
    • G. Papanicolaou and K. Sølna, Wavelet based estimation of local Kolmogorov turbulence, in Long-Range Dependence: Theory and Applications, eds. P. Doukhan, G. Oppenheim and M. S. Taqqu (Birkhäuser, 2002), pp. 473-506.
    • (2002) Long-Range Dependence: Theory and Applications , pp. 473-506
    • Papanicolaou, G.1    Sølna, K.2
  • 12
    • 0027373239 scopus 로고
    • Open-loop and closed-loop control of posture: A random walk analysis of center-of-pressure trajectories
    • J. J. Collins and C. J. De Luca, Open-loop and closed-loop control of posture: a random walk analysis of center-of-pressure trajectories, Exp. Brain Res. 9 (1993) 308-318.
    • (1993) Exp. Brain Res , vol.9 , pp. 308-318
    • Collins, J.J.1    De Luca, C.J.2
  • 13
    • 0031540977 scopus 로고    scopus 로고
    • Arbitrage with fractional Brownian motion
    • L. C. G. Rogers, Arbitrage with fractional Brownian motion, Math. Fin. 7 (1997) 95-105.
    • (1997) Math. Fin , vol.7 , pp. 95-105
    • Rogers, L.C.G.1
  • 14
    • 0242467551 scopus 로고    scopus 로고
    • Gaussian moving averages, semimartingales and option pricing
    • P. Cheridito, Gaussian moving averages, semimartingales and option pricing, Stochastic Process. Appl. 109(1) (2003) 47-68.
    • (2003) Stochastic Process. Appl , vol.109 , Issue.1 , pp. 47-68
    • Cheridito, P.1
  • 16
    • 1642419174 scopus 로고    scopus 로고
    • On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion
    • A. Ayache and J. Lévy Véhel, On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion, Stochastic Process. Appl. 111 (2004) 119-156.
    • (2004) Stochastic Process. Appl , vol.111 , pp. 119-156
    • Ayache, A.1    Lévy Véhel, J.2
  • 18
    • 0002188727 scopus 로고
    • Large-sample properties of parameter estimates for strongly dependent Gaussian time series
    • R. Fox and M. S. Taqqu, Large-sample properties of parameter estimates for strongly dependent Gaussian time series, Ann. Stat. 14 (1986) 517-532.
    • (1986) Ann. Stat , vol.14 , pp. 517-532
    • Fox, R.1    Taqqu, M.S.2
  • 19
    • 0001318609 scopus 로고
    • Efficient parameter estimation for self-similar processes
    • R. Dahlhaus, Efficient parameter estimation for self-similar processes, Ann. Stat. 17 (1989) 1749-1766.
    • (1989) Ann. Stat , vol.17 , pp. 1749-1766
    • Dahlhaus, R.1
  • 20
    • 0001898682 scopus 로고
    • A central limit theorem for quadratic forms in strongly dependent linear variables and its applications to the asymptotic normality of Whittle estimate
    • L. Giraitis and D. Surgailis, A central limit theorem for quadratic forms in strongly dependent linear variables and its applications to the asymptotic normality of Whittle estimate, Prob. Theory Rel. Fields. 86 (1990) 87-104.
    • (1990) Prob. Theory Rel. Fields , vol.86 , pp. 87-104
    • Giraitis, L.1    Surgailis, D.2
  • 21
    • 0026628466 scopus 로고
    • Wavelet analysis and synthesis of fractional Brownian motion
    • P. Flandrin, Wavelet analysis and synthesis of fractional Brownian motion, IEEE Trans. Inform. Theory 38 (1992) 910-917.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 910-917
    • Flandrin, P.1
  • 22
    • 14644410506 scopus 로고    scopus 로고
    • Self-similarity and long-range dependence through the wavelet lens
    • eds. P. Doukhan, G. Oppenheim and M. S. Taqqu Birkhäuser
    • P. Abry, P. Flandrin, M. Taqqu and D. Veitch, Self-similarity and long-range dependence through the wavelet lens, in Long-range Dependence: Theory and Applications, eds. P. Doukhan, G. Oppenheim and M. S. Taqqu (Birkhäuser, 2002), pp. 527-556.
    • (2002) Long-range Dependence: Theory and Applications , pp. 527-556
    • Abry, P.1    Flandrin, P.2    Taqqu, M.3    Veitch, D.4
  • 24
    • 33845704773 scopus 로고    scopus 로고
    • Identification of the multiscale fractional Brownian motion with biomechanical applications, to appear in J
    • J. M. Bardet and P. Bertrand, Identification of the multiscale fractional Brownian motion with biomechanical applications, to appear in J. Time Ser. Anal. 28 (2007) 1-52.
    • (2007) Time Ser. Anal , vol.28 , pp. 1-52
    • Bardet, J.M.1    Bertrand, P.2
  • 25
    • 0001249935 scopus 로고
    • A general version of the fundamental theorem of asset pricing
    • F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann. 300 (1994) 463-520.
    • (1994) Math. Ann , vol.300 , pp. 463-520
    • Delbaen, F.1    Schachermayer, W.2
  • 27
    • 0036539276 scopus 로고    scopus 로고
    • Statistical study of the wavelet analysis of fractional Brownian motion
    • J. M. Bardet, Statistical study of the wavelet analysis of fractional Brownian motion, IEEE Trans. Inform. Theory 48 (2002) 991-999.
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 991-999
    • Bardet, J.M.1


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