A central limit theorem for the generalized quadratic variation of the step fractional Brownian motion

Statistical Inference for Stochastic Processes

Volumn 10, Issue 1, 2007, Pages 1-27

  Ayache, Antoine ^a,b   Bertrand, Pierre ^c   Véhel, Jacques Lévy ^d  

^a UNIVERSITÉ LILLE 1   (France)

^b UNIV LILLE   (France)

^c UNIVERSITÉ BLAISE PASCAL   (France)

^d INRIA ROCQUENCOURT   (France)

Author keywords

Detection of abrupt changes; Generalized quadratic variation; Hurst index; Random wavelet series; Step fractional Brownian motion

Indexed keywords

EID: 33749515596     PISSN: 13870874     EISSN: 15729311     Source Type: Journal    
DOI: 10.1007/s11203-005-0532-2     Document Type: Article

References (16)

1. A. Ayache J. Lévy Véhel 2000 The generalized multifractional Brownian motion S.I.S.P. 3 1/2 7 18
2. J.M. Bardet 2000 Testing for the presence of self-similarity of Gaussian time series having stationary increments J. Time Ser. Anal. 21 497 516
3. Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., Peitgen, H.O., Saupe, D. and Voss, R.F.: The Science of Fractal Images, Springer Verlag, Berlin, 1988.
4. A. Benassi P. Bertrand S. Cohen J. Istas 2000 Identification of the Hurst index of a step fractional brownian motion S.I.S.P. 3 1/2 101 111
5. A. Benassi S. Jaffard D. Roux 1997 Elliptic Gaussian random processes Rev. Mathemàtica Iberoamericana 13 1 19 90
6. P. Bertrand 2000 A local method for estimating change points: the hat-function Statistics 34 215 235
7. Bertrand, P. and Bardet, J.M.: Some generalization of fractional Brownian motion and control. In: J.L. Menaldi, E. Rofman and A. Sulem (eds), Optimal Control and Partial Differential Equations, IOS Press, Amsterdam, (2001), 221-230.
8. P. Cheridito 2003 Arbitrage in fractional Brownian motion models Finance and Stochastics 7 4 533 553
9. Davydov, Y., Khoshnevisan, D., Shi, Z. and Zitikis, R.: Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data, to appear in J. of Statistical Planning and Inference.
10. X. Guyon J.R. Leon 1989 Convergence en loi des H-variations d'un processus gaussien fractionnaire Ann. Inst. H. Poincaré 25 3 265 282
11. J. Istas G. Lang 1997 Quadratic variation and estimation of the local Hölder index of a Gaussian process Ann. Inst. H. Poincaré 33 4 407 437
12. A.N. Kolmogorov 1940 Wienersche Spiralen und einige andere interessante Kurven in Hilbertchen Raume Doklady 26 115 118
13. B. Mandelbrot J. Van Ness 1968 Fractional Brownian motion, fractional noises and applications SIAM Rev. 10 422 437
14. Papanicolaou, G. and Sølna, K.: Wavelet based estimation of local Kolmogorov turbulence. In: P. Doukhan, G. Oppenheim and M.S. Taqqu (eds), Long-range Dependence: Theory and Applications, Birkhäuser, Basel, 2002, 473-506.
15. Peltier, R. and Lévy Véhel, J.: Multifractional Brownian motion: definition and preliminary results, Rapport technique INRIA, 1996.
16. Samorodnitsky, G. and Taqqu M. S.: Stable Non-Gaussian Random Processes, Chapman & Hall, London, 1994.