## 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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