Hausdorff Dimension of Operator Stable Sample Paths

Monatshefte fur Mathematik

Volumn 140, Issue 2, 2003, Pages 91-101

  Becker Kern, Peter ^a   Meerschaert, Mark M ^b   Scheffler, Hans Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

^b UNIVERSITY OF NEVADA   (United States)

Author keywords

Hausdorff dimension; Operator stable; Sample path

Indexed keywords

EID: 0242677810     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-002-0534-8     Document Type: Article

References (23)

1. Ashbaugh M, Rajput BS, Rama-Murthy K, Sundberg C (1992) Remarks on the positivity of densities of stable laws. Prob Math Stat 13: 77-86
2. Benson D, Schumer R, Meerschaert M, Wheatcraft S (2001) Fractional dispersion, Lévy motions, and the MADE tracer tests. Transport in Porous Media 42: 211-240
3. Benson D, Wheatcraft S, Meerschaert M (2000) Application of a fractional advection-dispersion equation. Water Resources Research 36: 1403-1412
4. Benson D, Wheatcraft S, Meerschaert M (2000) The fractional-order governing equation of Lévy motion. Water Resources Research 36: 1413-1424
5. Blumenthal RM, Getoor RK (1960) A dimension theorem for sample functions of stable processes. Illinois J Math 4: 370-375
6. Hendricks WJ (1983) A uniform lower bound for the Hausdorff dimension for transient symmetric Lévy processes. Ann Probab 11: 589-592
7. Hudson W, Mason JD (1982) Operator-self-similar processes in a finite-dimensional space. Trans Amer Math Soc 273: 281-297
8. Jurek Z, Mason JD (1993) Operator-Limit Distributions in Probability Theory. Wiley: New York
9. Meerschaert M (1990) Moments of random vectors which belong to some domain of normal attraction. Ann Probab 18: 870-876
10. Meerschaert M (1991) Spectral decomposition for generalized domains of attraction. Ann Probab 19: 875-892
11. Meerschaert M, Scheffler HP (2001) Limit Distributions for Sums of Independent Random Vectors. Wiley: New York
12. Meerschaert M, Scheffler HP (2001) Portfolio modeling with heavy tailed random vectors. In: Handbook of Heavy-Tailed Distributions in Finance (to appear)
13. Meerschaert M, Benson DA, Baeumer B (2001) Operator Lévy motion and multiscaling anomalous diffusion. Phys Rev E 63: 021112-021117
14. Port SC, Vitale RA (1988) Positivity of stable densities. Proc Amer Math Soc 102: 1018-1023
15. Pruitt WE (1969) The Hausdorff dimension of the range of a process with stationary independent increments. J Math Mech 19: 371-378
16. Pruitt WE, Taylor SJ (1969) Sample path properties of processes with stable components. Z Wahrsch verw Geb 12: 267-289
17. Rajput BS (1993) Supports of certain infinitely divisible probability measures on locally convex spaces. Ann Probab 21: 886-897
18. Rogers CA, Taylor SJ (1959) The analysis of additive set functions in Euclidean space. Acta Math 101: 273-302
19. Taylor SJ (1986) The measure theory of random fractals. Math Proc Cambridge Philos Soc 100: 383-406
20. Taylor SJ (1967) Sample path properties of transient stable processes. J Math Mech 16: 1229-1246
21. Taylor SJ (1986) The use of packing measure in the analysis of random sets. In: Stochastic Processes and Their Applications (Nagoya, 1985). Lect Notes Math 1203, 214-222. Berlin Heidelberg New York: Springer
22. Wheatcraft SW, Tyler S (1988) An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour Res 24: 566-578
23. Zolotarev VM (1986) One-Dimensional Stable Distributions. Providence, Rhode Island: Amer Math Soc