Article PDF
Avoid common mistakes on your manuscript.
References
Blumenthal, R. M., and R. K. Getoor: A dimension theorem for sample functions of stable processes. Illinois J. Math. 4, 370–375 (1960).
— —: The dimension of the set of zeros and the graph of a symmetric stable process. Illinois J. Math. 6, 308–316 (1962).
— —, and H. P. McKean: Markov processes with identical hitting probabilities. Illinois J. Math. 6, 402–420 (1962).
Brelot, M.: Lectures on potential theory. Tata Institute, Bombay 1960.
Ciesielski, Z., and S. J. Taylor: First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. math. Soc. 103, 434–450 (1962).
Dvoretzky, A., P. Erdös, and S. Kakutani: Double points of paths of Brownian motion in n-space. Acta Sci. math. 12 M, 75–81 (1950).
— — —: Multiple points of paths of Brownian motion in the plane. Bull Res. Council Israel Sect. F 3, 364–371 (1954).
— — —, and S. J. Taylor: Triple points of Brownian motion in 3-space. Proc. Cambridge philos. Soc. 53, 856–862 (1957).
— — —: Points of multiplicity c of plane Brownian paths. Bull Res. Council Israel Sect. F 7, 175–180 (1958).
Getoor, R. K.: Additive functionals and excessive functions. Ann. math. Statistics 36, 409–422 (1965).
Hunt, G. A.: Markov processes and potentials. Illinois J. Math. 1, 42–93 and 316–369 (1957), also 2, 151–213 (1958).
Lévy, P.: Processes stochastiques et mouvement brownian. Paris 1948.
McKean, H. P.: Sample functions of stable processes. Ann. of Math. II. Ser. 61, 564–579 (1955).
Spitzer, F.: Some theorems concerning 2-dimensional Brownian motion. Trans. Amer. math. Soc. 87, 187–197 (1958).
Stein, C.: A note on cumulative sums. Ann. math. Statistics 17, 498–499 (1946).
Takeucki, J.: On the sample paths of the symmetric stable processes in spaces. Jour. math. Soc. Japan 16, 109–127 (1964).
—, and S. Watanabe: Spitzer's test for the Cauchy process on the line. Z. Wahrscheinlichkeitstheorie verw. Geb. 3, 204–210 (1964).
Taylor, S. J.: On the connection between Hausdorff measures and generalized capacities. Proc. Cambridge philos. Soc. 57, 524–531 (1961).
—: The exact Hausdorff measure of the sample path for planar Brownian motion. Proc. Cambridge philos. Soc. 60, 253–258 (1964).
Author information
Authors and Affiliations
Additional information
During the preparation of this paper the author was supported by the National Science Foundation, NSF-GP3754.
Rights and permissions
About this article
Cite this article
Taylor, S.J. Multiple points for the sample paths of the symmetric stable process. Z. Wahrscheinlichkeitstheorie verw Gebiete 5, 247–264 (1966). https://doi.org/10.1007/BF00533062
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00533062