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Self-intersections of random fields. (English) Zbl 0536.60066

This paper gives Hausdorff dimension results for the r-multiple times of Brownian motions, Brownian sheets and the general multiparametric Gaussian process \(W^{\beta}(t)\) with mean zero and \(E(W^{\beta}(s)- W^{\beta}(t))^ 2=| s-t|^{2\beta}\), \(0<\beta<1\). The main result is that for index \(\beta\) processes from \(R^ N\to R^ d\), the Hausdorff dimension of the r-multiple points is Nr-\(\beta\) d(r-1) when this quantity is positive.
Reviewer: J.Cuzick

MSC:

60G60 Random fields
60G17 Sample path properties
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