Khoshnevisan, Davar Some polar sets for the Brownian sheet. (English) Zbl 0886.60039 Azéma, J. (ed.) et al., Séminaire de probabilités XXXI. Berlin: Springer. Lect. Notes Math. 1655, 190-197 (1997). The author deals with the sets that are avoided by the path of \(d\)-dimensional \(N\)-parameter Brownian sheet \(W\). In the language of Markov processes, such sets are said to be polar. It is said that \(W\) has \(k\)-multiple points, if there exist \(k\) distinct times \(t^1, \dots, t^k\) from \(R^N_+\) such that \(W(t^1)= \cdots= W(t^k)\). The main result is: The probability that \(W\) has \(k\)-multiple points is 1 or 0 according whether \((d-2N) k<d\) or \((d-2N) k>d\). The paper contains an extended bibliography devoted to the history of the problem.For the entire collection see [Zbl 0864.00069]. Reviewer: Yu.S.Mishura (Kyïv) Cited in 7 Documents MSC: 60G60 Random fields 60J65 Brownian motion Keywords:\(N\)-parameter Brownian sheet; polar set PDFBibTeX XMLCite \textit{D. Khoshnevisan}, Lect. Notes Math. 1655, 190--197 (1997; Zbl 0886.60039) Full Text: Numdam EuDML