Rosen, Jay Self-intersections of random fields. (English) Zbl 0536.60066 Ann. Probab. 12, 108-119 (1984). 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 Cited in 3 ReviewsCited in 28 Documents MSC: 60G60 Random fields 60G17 Sample path properties Keywords:local time; self intersection; Hausdorff dimension; Brownian sheets; multiple points PDF BibTeX XML Cite \textit{J. Rosen}, Ann. Probab. 12, 108--119 (1984; Zbl 0536.60066) Full Text: DOI OpenURL