References
S. M. Berman, Gaussian processes with stationary increments: local times and sample function properties,Ann. Math. Statist.,41, 1260–1272 (1970).
A. Dvoretzky, P. Erdös, and S. Kakutani, Double points of paths of Brawnian motion inn-space,Acta Sci. Math. (Szeged),12, 75–81 (1950).
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).
A. Dvoretzky, P. Erdös, and S. Kakutani, Triple points of Brownian paths in 3 spaces,Proc. Cambridge Philos. Soc.,53, 856–862 (1957).
J. Cuzick, Multiple points of a Gaussian vector field,Z. Wahrsch. verw. Geb.,61, 431–436 (1982).
K. J. Falconer, The geometry of fractal sets,Cambridge Fracts in Math., p. 185 (1985).
J. Hawkes, Multiple points for symmetric Lévy processes,Math. Proc. Cambridge Philos. Soc.,83, 83–90 (1978).
W. J. Hendricks, Multiple points for transient symmetric Lévy processes in ℝd,Z. Wahrsch. verw. Geb.,49, 13–21 (1979).
A. Goldman, Points multiples des trajectoires de processus Gaussiens,Z. Wahrsch. verw. Geb.,57, 481–494 (1981).
J. Hawkes, Some dimension theorems for the sample functions of stable processes,Indiana Univ. Math. J.,20, 733–738 (1971).
N. Kalinauskaitė, On multiple points of some stable random fields,Lithuanian Math. J.,31, 127–135 (1991).
N. Kôno, Double points of Gaussian sample paths,Z. Wahrsch. verw. Geb.,45, 175–180 (1978).
M. B. Marcus, Capacity of level sets of certain stochastic processes,Z. Wahrsch. verw. Geb.,34, 279–284 (1976).
J. Nolan, Path properties of index-β stable fields,Ann. Probab.,16, 1596–1607 (1988).
J. Nolan, Local nondeterminism and local times for stable processes,Probab. Rel. Fields,82, 387–410 (1989).
S. J. Taylor, Multiple points for the sample paths of the symmetric stable processes,Z. Wahrsch. verw. Geb.,5, 247–266 (1966).
M. Weber, Dimension de Hausdorff et points multiples du mouvement Brownian fractionaire dans ℝd,C.R. Acad. Sci. Paris,297, 357–360 (1983).
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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.
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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
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DOI: https://doi.org/10.1007/BF00970973