Contours of Brownian processes with several-dimensional times
- Cite this article as:
- Kendall, W.S. Z. Wahrscheinlichkeitstheorie verw Gebiete (1980) 52: 267. doi:10.1007/BF00538891
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Two generalisations of Brownian motion to several-dimensional time are considered and the topology of their level sets is analysed. It is shown that for these maps non-trivial contours are quite rare — their union has Lebesgue measure zero. The boundedness of all contours is established for the generalisation due to Lévy. For the other, the Brownian sheet, a partial result concerning the behaviour of the zero contour near the boundary is established.