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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].

MSC:

60G60 Random fields
60J65 Brownian motion
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