Path properties of the linear multifractional stable motion

Fractals

Volumn 13, Issue 2, 2005, Pages 157-178

  Stoev, Stilian ^a   Taqqu, Murad S ^a  

^a Boston University   (United States)

Author keywords

Heavy Tails; H lder Regularity; Linear Fractional Stable Motion; Local Self Similarity; Multifractional Brownian Motion; Path Continuity; Self Similarity

Indexed keywords

ASYMPTOTIC STABILITY; BROWNIAN MOVEMENT; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; CORRELATION METHODS; FUNCTIONS; LINEAR SYSTEMS; RANDOM PROCESSES;

HEAVY TAILS; HÖLDER REGULARITY; LINEAR MULTIFRACTIONAL STABLE MOTION (LMSM); LOCAL SELF-SIMILARITY; MULTIFRACTIONAL BROWNIAN MOTION (MBM); PATH CONTINUITY; PATH PROPERTIES; SELF-SIMILARITY;

FRACTALS;

EID: 21144433639     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X05002775     Document Type: Article

References (23)

1. S. Stoev and M. S. Taqqu, Stochastic properties of the linear multifractional stable motion, Adv. Appl. Probab. 36(4) (2004) 1085-1115.
2. R. F. Peltier and J. L. Levy-Vehel, Multifractional Brownian Motion: Definition and Preliminary Results, Technical Report 2645 (Institut National de Recherche en Informatique et an Automatique, INRIA, Le Chesnay, France, 1995).
3. A. Benassi, S. Jaffard and D. Roux, Elliptic Gaussian random processes, Rev. Math. Iberoam. 13(1) (1997) 19-90.
4. A. Ayache and J. Lévy-Véhel, The generalized multifractional Brownian motion, Stat. Inf. Stock. Process. 3 (2000) 7-18.
5. A. Ayache, The generalized multifractional field: a nice tool for the study of the generalized multifractional Brownian motion, J. Fourier Anal. Appl. 8(6) (2002) 581-601.
6. A. Ayache and M. S. Taqqu, Multifractional processes with random exponent, preprint (2003).
7. M. S. Taqqu Fractional Brownian motion and long-range dependence, in Theory and Applications of Long-Range Dependence, eds. P. Doukhan, G. Oppenheim and M. S. Taqqu, (Birkhäuser, 2003) pp. 5-38.
8. P. Embrechts and M. Maejima, Self-Similar Processes (Academic Press, 2003).
9. S. Cohen, From self-similarity to local self-similarity: the estimation problem, in Fractals: Theory and Applications in Engineering, eds. M. Dekking, J. L. Véhel, E. Lutton and C. Tricot, (Springer-Verlag, 1999).
10. S. Stoev and M. S. Taqqu, How rich is the class of multifractional Brownian motions?, Preprint (2004).
11. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance (Chapman and Hall, New York, London, 1994).
12. A. Benassi, S. Cohen and J. Istaa, Identification and properties of real harmonizable fractional Lévy motions, Bernoulli 8 (2002) 97-115.
13. A. Benassi, S. Cohen and J. Istas, On roughness indices for fractional fields, Bernoulli 10(2) (2004) 357-373.
14. J.-M. Bardet and P. Bertrand, Properties and identification of the multiscale fractional Brownian motion with biomedical applications, preprint (2003).
15. J. L. Doob, Stochastic Processes (Wiley, New York, 1953).
16. D. W. Stroock, Probability Theory: An Analytic View (Cambridge University Press, New York, 1993).
17. S. Seuret and J. Lévy-Vehel, The local Hölder function of a continuous function, Appl. Comput. Harm. Anal. 13(3) (2002) 263-276.
18. B. Guiheneuf and J. Lévy-Vehel, Two-microlocal analysis and applications in signal processing, in Wavelets and Multiscale Methods, International Wavelets Conference (INRIA, Tangier, Morocco, 1998).
19. S. Jaffard and Y. Meyer, Wavelet methods for pointwise regularity and local oscillations of functions, in Memoirs of the American Mathematical Society, Vol. 587 (American Mathematical Society, Providence, RI, 1996).
20. B. Guiheneuf, S. Jaffard and J. Lévy-Vehel, Two results concerning chirps and 2-microlocal exponents prescription, Appl. Comput. Harm. Anal. 5(4) (1998) 487-492.
21. I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, in Graduate Texts in Mathematics, 2nd edn, Vol. 113 (Springer-Verlag, New York, 1991).
22. A. Ayache, S. Jaffard and M. S. Taqqu, Multifractional processes with most general Hölder exponents, preprint (2003).
23. H. L. Royden, Real Analysis, 3rd edn. (Macmillan, 1998).