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Contours of Brownian processes with several-dimensional times. (English) Zbl 0431.60056


MSC:

60G60 Random fields
60J65 Brownian motion
60F20 Zero-one laws
Full Text: DOI

References:

[1] Adler, R. J., The uniform dimension of the level sets of a Brownian Sheet, Ann. Probability, 6, 509-515 (1978) · Zbl 0378.60028
[2] Čentsov, N. N., Wiener random fields depending on several parameters, Dokl. Akad. Nauk. S.S.S.R. (NS), 106, 607-609 (1956) · Zbl 0074.12503
[3] Čentsov, N. N., Lévy Brownian motion for several parameters and generalized white noise, Theor. Probability Appl., 2, 265-266 (1957)
[4] Freedman, D., Brownian motion (1971), San Francisco: Holden Day, San Francisco · Zbl 0231.60072
[5] Hurewicz, W., Wallman, H.: Dimension Theory. Princeton University Press 1941 · JFM 67.1092.03
[6] McKean, H. P. Jr., Brownian motion with a several-dimensional time, Theor. Probability Appl., 8, 335-354 (1963) · Zbl 0124.08702
[7] Molčan, G. M., On some problems concerning Brownian motion in Levy’s sense, Theor. Probability Appl., 12, 682-690 (1967) · Zbl 0159.46504
[8] Orey, S.; Pruitt, W. E., Sample functions of the N-parameter Wiener process, Ann. Probability, 1, 138-163 (1973) · Zbl 0284.60036
[9] Park, W. J., A multiparameter Gaussian process, Ann. Math. Statist., 41, 1582-1595 (1970) · Zbl 0279.60030
[10] Pitt, L. D.; Tran, L. T., Local sample path properties of Gaussian fields, Ann. Probability, 7, 477-493 (1979) · Zbl 0401.60035
[11] Pyke, R.; Kendall, D. G.; Harding, E. F., Partial sums of matrix arrays, and Brownian sheets, Stochastic Analysis, 331-348 (1973), London-New York: Wiley, London-New York
[12] Tran, L. T., Local maxima of the sample functions of the 2-parameter Wiener process, Proc. Amer. Math. Soc., 58, 250-254 (1976) · Zbl 0312.60020
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