Skip to main content
Log in

On the Hausdorff dimension of a set of multiple points for some stable random fields

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. M. Berman, Gaussian processes with stationary increments: local times and sample function properties,Ann. Math. Statist.,41, 1260–1272 (1970).

    Google Scholar 

  2. A. Dvoretzky, P. Erdös, and S. Kakutani, Double points of paths of Brawnian motion inn-space,Acta Sci. Math. (Szeged),12, 75–81 (1950).

    Google Scholar 

  3. A. Dvoretzky, P. Erdös, and S. Kakutani, Multiple points of paths Brownian motion in the plane,Bull. Research Council of Israel, Section F,3, 364–371 (1954).

    Google Scholar 

  4. A. Dvoretzky, P. Erdös, and S. Kakutani, Triple points of Brownian paths in 3 spaces,Proc. Cambridge Philos. Soc.,53, 856–862 (1957).

    Google Scholar 

  5. J. Cuzick, Multiple points of a Gaussian vector field,Z. Wahrsch. verw. Geb.,61, 431–436 (1982).

    Google Scholar 

  6. K. J. Falconer, The geometry of fractal sets,Cambridge Fracts in Math., p. 185 (1985).

  7. J. Hawkes, Multiple points for symmetric Lévy processes,Math. Proc. Cambridge Philos. Soc.,83, 83–90 (1978).

    Google Scholar 

  8. W. J. Hendricks, Multiple points for transient symmetric Lévy processes in ℝd,Z. Wahrsch. verw. Geb.,49, 13–21 (1979).

    Google Scholar 

  9. A. Goldman, Points multiples des trajectoires de processus Gaussiens,Z. Wahrsch. verw. Geb.,57, 481–494 (1981).

    Google Scholar 

  10. J. Hawkes, Some dimension theorems for the sample functions of stable processes,Indiana Univ. Math. J.,20, 733–738 (1971).

    Google Scholar 

  11. N. Kalinauskaitė, On multiple points of some stable random fields,Lithuanian Math. J.,31, 127–135 (1991).

    Google Scholar 

  12. N. Kôno, Double points of Gaussian sample paths,Z. Wahrsch. verw. Geb.,45, 175–180 (1978).

    Google Scholar 

  13. M. B. Marcus, Capacity of level sets of certain stochastic processes,Z. Wahrsch. verw. Geb.,34, 279–284 (1976).

    Google Scholar 

  14. J. Nolan, Path properties of index-β stable fields,Ann. Probab.,16, 1596–1607 (1988).

    Google Scholar 

  15. J. Nolan, Local nondeterminism and local times for stable processes,Probab. Rel. Fields,82, 387–410 (1989).

    Google Scholar 

  16. S. J. Taylor, Multiple points for the sample paths of the symmetric stable processes,Z. Wahrsch. verw. Geb.,5, 247–266 (1966).

    Google Scholar 

  17. M. Weber, Dimension de Hausdorff et points multiples du mouvement Brownian fractionaire dans ℝd,C.R. Acad. Sci. Paris,297, 357–360 (1983).

    Google Scholar 

Download references

Authors

Additional information

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 1, pp. 71–79, January–March, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kalinauskaitė, N. On the Hausdorff dimension of a set of multiple points for some stable random fields. Lith Math J 32, 54–60 (1992). https://doi.org/10.1007/BF00970973

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970973

Keywords

Navigation