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Wiener path intersections and local time. (English) Zbl 0403.60069


MSC:

60J55 Local time and additive functionals
60J65 Brownian motion
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References:

[1] Blumenthal, R. M.; Getoor, R. K., Markov Processes and Potential Theory (1968), Academic Press: Academic Press New York · Zbl 0169.49204
[2] Ciesielski, E.; Taylor, S. J., 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) · Zbl 0121.13003
[3] Doob, J. L., Stochastic Processes (1953), Wiley: Wiley New York · Zbl 0053.26802
[4] Dvoretsky, A.; Erdös, P.; Kakutani, S., Multiple points of paths of Brownian motion in the plane, Bull. Res. Counc. Israel, 3, 364-371 (1954)
[5] Federer, H., Geometric Measure Theory (1969), Springer-Verlag: Springer-Verlag New York · Zbl 0176.00801
[6] Hawkes, J., On the Hausdorff dimension of the intersection of the range of a stable, process with a Borel set, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 19, 90-102 (1971) · Zbl 0203.49903
[7] Hunt, G. A., Some theorems concerning Brownian motion, Trans. Amer. Math. Soc., 81, 294-319 (1956) · Zbl 0070.36601
[8] Itô, K.; McKean, H. P., Diffusion Processes and Their Sample Paths (1965), Springer-Verlag: Springer-Verlag Berlin · Zbl 0127.09503
[9] Kaufman, R., Une propriété métrique du mouvement brownien, C. R. Acad. Sci. Paris Sér. A, 268, 727-728 (1969) · Zbl 0174.21401
[10] Simon, B., The \(P(φ)_2\) Euclidean (Quantum) Field Theory (1974), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 1175.81146
[11] Taylor, S. J., The Hausdorff α-dimensional measure of Brownian paths in \(n\)-space, (Proc. Cambridge Philos. Soc., 49 (1953)), 31-39 · Zbl 0050.05803
[12] Taylor, S. J., The exact Hausdorff measure of the sample path for planar Brownian motion, (Proc. Cambridge Philos. Soc., 60 (1964)), 253-258 · Zbl 0149.13104
[13] Taylor, S. J., Multiple points for the sample paths of the symmetric stable process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 5, 247-264 (1966) · Zbl 0146.37905
[14] Wolpert, R., Local time and a partical picture for Euclidean field theory, J. Functional Analysis, 30, 341-357 (1978) · Zbl 0464.70016
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