Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 13 (2008) > Paper 29 open journal systems 


Path properties of a class of locally asymptotically self similar processes

Brahim Boufoussi, Cadi Ayyad University
Marco E. Dozzi, Nancy University
Raby Guerbaz, Cadi Ayyad University


Abstract
Various paths properties of a stochastic process are obtained under mild conditions which allow for the integrability of the characteristic function of its increments and for the dependence among them. The main assumption is closely related to the notion of local asymptotic self-similarity. New results are obtained for the class of multifractional random processes.


Full text: PDF

Pages: 898-921

Published on: May 9, 2008


Bibliography
  1. Adler, Robert J. The geometry of random fields.Wiley Series in Probability and Mathematical Statistics.John Wiley & Sons, Ltd., Chichester, 1981. xi+280 pp. ISBN: 0-471-27844-0 MR0611857 (82h:60103)
  2. Benassi, Albert; Cohen, Serge; Istas, Jacques. Identification and properties of real harmonizable fractional Lévy motions. Bernoulli 8 (2002), no. 1, 97--115. MR1884160 (2003b:60075)
  3. Benassi, Albert; Cohen, Serge; Istas, Jacques. Identifying the multifractional function of a Gaussian process. Statist. Probab. Lett. 39 (1998), no. 4, 337--345. MR1646220 (99h:60080)
  4. Benassi, Albert; Cohen, Serge; Istas, Jacques; Jaffard, Stéphane. Identification of filtered white noises. Stochastic Process. Appl. 75 (1998), no. 1, 31--49. MR1629014 (99e:60104)
  5. Benassi, Albert; Cohen, Serge; Istas, Jacques. Local self-similarity and the Hausdorff dimension. C. R. Math. Acad. Sci. Paris 336 (2003), no. 3, 267--272. MR1968271 (2004b:60110)
  6. Benassi, Albert; Jaffard, Stéphane; Roux, Daniel. Elliptic Gaussian random processes. Rev. Mat. Iberoamericana 13 (1997), no. 1, 19--90. MR1462329 (98k:60056)
  7. Berman, Simeon M. Gaussian processes with stationary increments: Local times and sample function properties. Ann. Math. Statist. 41 1970 1260--1272. MR0272035 (42 #6916)
  8. Berman, S. M. (1969), Harmonic analysis of local times and sample functions of Gaussian processes, Trans. Amer. Math. Soc. 143, 269-281.
  9. Berman, Simeon M. Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J. 23 (1973/74), 69--94. MR0317397 (47 #5944)
  10. Berman, Simeon M. Local nondeterminism and local times of general stochastic processes. Ann. Inst. H. Poincaré Sect. B (N.S.) 19 (1983), no. 2, 189--207. MR0700709 (85b:60041)
  11. Berman, Simeon M. The modulator of the local time. Comm. Pure Appl. Math. 41 (1988), no. 1, 121--132. MR0917127 (89d:60074)
  12. Berman, Simeon M. Self-intersections and local nondeterminism of Gaussian processes. Ann. Probab. 19 (1991), no. 1, 160--191. MR1085331 (92d:60047)
  13. Boufoussi, B.; Dozzi, M.; Guerbaz, R. On the local time of multifractional Brownian motion. Stochastics 78 (2006), no. 1, 33--49. MR2219711 (2007m:60239)
  14. Boufoussi, Brahim; Dozzi, Marco; Guerbaz, Raby. Sample path properties of the local time of multifractional Brownian motion. Bernoulli 13 (2007), no. 3, 849--867. MR2348754
  15. Cheridito, Patrick. Mixed fractional Brownian motion. Bernoulli 7 (2001), no. 6, 913--934. MR1873835 (2002k:60163)
  16. Cohen, Serge. From self-similarity to local self-similarity: the estimation problem. Fractals: theory and applications in engineering, 3--16, Springer, London, 1999. MR1726364 (2001c:60063)
  17. Falconer, Kenneth J. Tangent fields and the local structure of random fields. J. Theoret. Probab. 15 (2002), no. 3, 731--750. MR1922445 (2003g:60017)
  18. Föllmer, Hans; Wu, Ching-Tang; Yor, Marc. On weak Brownian motions of arbitrary order. Ann. Inst. H. Poincaré Probab. Statist. 36 (2000), no. 4, 447--487. MR1785391 (2001k:60114)
  19. Geman, Donald. A note on the continuity of local times. Proc. Amer. Math. Soc. 57 (1976), no. 2, 321--326. MR0420812 (54 #8824)
  20. Geman, Donald; Horowitz, Joseph. Occupation densities. Ann. Probab. 8 (1980), no. 1, 1--67. MR0556414 (81b:60076)
  21. Guerbaz, Raby. Local time and related sample paths of filtered white noises. Ann. Math. Blaise Pascal 14 (2007), no. 1, 77--91. MR2298805
  22. Guerbaz, Raby. Hölder conditions for the local times of multiscale fractional Brownian motion. C. R. Math. Acad. Sci. Paris 343 (2006), no. 8, 515--518. MR2267586 (2007m:60241)
  23. Kono, N. and Shieh, N.R. (1993), Local times and related sample path properties of certain self-similar processes, J. Math. Kyoto Univ. 33, 51-64.
  24. Lévy-Véhel, J. and Peltier, R.F. (1995), Multifractional Brownian motion : definition and preliminary results, rapport de l'INRIA 2645.
  25. Nolan, John P. Local nondeterminism and local times for stable processes. Probab. Theory Related Fields 82 (1989), no. 3, 387--410. MR1001520 (91b:60060)
  26. Pitt, Loren D. Local times for Gaussian vector fields. Indiana Univ. Math. J. 27 (1978), no. 2, 309--330. MR0471055 (57 #10796)
  27. Shieh, Narn-Rueih. Limit theorems for local times of fractional Brownian motions and some other self-similar processes. J. Math. Kyoto Univ. 36 (1996), no. 4, 641--652. MR1443740 (98f:60077)
  28. Stoev, Stilian; Taqqu, Murad S. Path properties of the linear multifractional stable motion. Fractals 13 (2005), no. 2, 157--178. MR2151096 (2006d:60082)
  29. Stoev, Stilian; Taqqu, Murad S. Stochastic properties of the linear multifractional stable motion. Adv. in Appl. Probab. 36 (2004), no. 4, 1085--1115. MR2119856 (2005m:60079)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489