On fractional Gaussian random fields simulations

Journal of Statistical Software

Volumn 23, Issue 1, 2007, Pages 1-23

  Brouste, Alexandre ^a,c   Istas, Jacques ^b,d   Lambert Lacroix, Sophie ^b,d  

^a Université du Maine

^b UNIV GRENOBLE ALPES   (France)

^c Laboratoire de Statistique et Processus   (France)

^d UNIV GRENOBLE ALPES   (France)

Author keywords

Gaussian fields; H lder index; Simulation

Indexed keywords

EID: 38549090205     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v023.i01     Document Type: Article

References (31)

1. Ayache A, Léger S, Pontier M (2002). "Drap Brownien Fractionnaire." Potential Analysis, 17, 31-43.
2. Ayache A, Lévy-Vehel J (2000). "The Multifractional Brownian Motion." Statistical Inference for Stochastic Process, 1, 7-18.
3. Bardet J, Lang G, Oppenheim G, Philippe A, Taqqu M (2003). "Generators of the Long-range Dependence Processes: A Survey." In M Taqqu, G Oppenheim, P Doukhan (eds.), "Long range dependence," pp. 579-624. Birkhaüser.
4. Bégyn A (2006). Generalized Quadratic Variations of Gaussian Processes: Limit Theorems and Applications to Fractional Processes. Ph.D. thesis, Université de Toulouse.
5. Benassi A, Bertrand P, Cohen S, Istas J (2000). "Identification of the Hurst Index of a Step Fractional Brownian Motion." Statistical Inference for Stochastic Process, 3, 101-111.
6. Benassi A, Cohen S, Istas J (1998). "Identifying the Multifractional Function of a Gaussian Process." Statistics and Probability Letters, 39, 337-345.
7. Benassi A, Jaffard S, Roux D (1997). "Elliptic Gaussian Random Processes." Revista Mathematica Iberoamericana, 18, 19-89.
8. Biermé H (2005). Champs Aléatoires : Autosimilarité, Anisotropie et Etude Directionnelle. Ph.D. thesis, Université d'Orléans.
9. Bonami A, Estrade A (2004). "Anisotropic Analysis of Gaussian models." Journal of Fourier Analysis and Applications, 9, 215-236.
10. Coeurjolly J (2000). "Simulation and Identification of the Fractional Brownian Motion: A Bibliographical and Comparative Study." Journal of Statistical Software, 5(7), 1-53. URL http ://www.jstatsoft.org/v05/i07.
11. Dégerine S, Lambert-Lacroix S (2003). "Partial Autocorrelation Function of a Nonstationary Time Series." Journal of Multivariate Analysis, 87(1), 46-59.
12. Fournier A, Fussel D, Carpenter L (1982). "Computer Rendering of Stochastic Models." Communication of the AMC, 25, 371-384.
13. Frisch U, Parisi G (1985). "Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics." In M Ghil, R Benzi, G Parisi (eds.), "Proceedings of the International School of Physics E. Fermi," pp. 84-88. North-Holland.
14. Helgason S (1962). Differential Geometry and Symmetric Spaces. Academic Press.
15. Herbin E (2006). "From N-parameter Fractional Brownian Motions to N-parameter Multifractional Brownian Motion." Rocky Mountain Journal of Mathematics, 3, 1249-1284.
16. Houdré C, Villa J (2003). "An Example of Infinite Dimensional Quasi-Helix." Contemporary Mathematics, AMS, 336, 195-201.
17. Istas J (2005). "Spherical and Hyperbolic Fractional Brownian Motion." Electronic Journal of Probability, 10, 254-262.
18. Istas J, Lang G (1997). "Quadratic Variations and Estimation of the Local Holder Index of a Gaussian Process." Annales Institut Henri Poincaré, Probabilités et Statistiques, 33, 407-436.
19. Kamont A (1996). "On the Fractional Anisotropic Wiener Fields." Journal of Probability and Mathematical Statistics, 18, 85-98.
20. Kolmogorov A (1940). "Wienersche Spiralen und Einige Andere Interessante Kurven im Hilbertsche Raum. (German)." C. R. (Doklady) Academy of Sciences URSS, 26, 115-118.
21. Lacaux C (2004). "Real Harmonizable Multifractional Lévy Motions." Annales Institut Henri Poincaré, Probabilités et Statistiques, 40, 259-277.
22. Leland W, Taqqu M, Willinger W, Wilson V (1994). "On the Self-Similar Nature of Ethernet Traffic (Extended Version)." IEEE/ACM Transactions on Networking, 2(1), 1-15.
23. Levy P (1965). Processus Stochastiques et Mouvement Brownien. Gauthier-Villars.
24. Mandelbrot B (1975). "Stochastic Models for the Earth's Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands." In "Proceedings of the National Academy of Sciences," 10, pp. 3825-3828.
25. Mandelbrot B, Ness JV (1968). "Fractional Brownian Motions, Fractional Noises and Application." SIAM Review, 10, 422-437.
26. Peitgen H, Saupe D (1988). The Science of Fractal Images. Springer-Verlag.
27. Peltier R, Levy-Véhel J (1996). "Multifractional Brownian Motion: Definition and Preliminary Results." Technical Report RR 2645, INRIA. URL http://hal.inria.fr/ inria-00074045/fr/.
28. Pentland A (1984). "Fractal-based Description of Natural Scenes." IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 661-674.
29. R Development Core Team (2007). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http: //www.R-project.org/.
30. Samorodnitsky G, Taqqu M (1994). Stable non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, New York.
31. Voss R (1985). "Random Fractal Forgeries." NATO ASI Series, F17, 805-835.