Summary.
It is well-known that Brownian motion has no points of increase. We show that an analogous statement for the Brownian sheet is false. More precisely, for the standard Brownian sheet in the positive quadrant, we prove that there exist monotone curves along which the sheet has a point of increase.
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Received: 7 December 1994 / In revised form: 6 August 1996
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Dalang, R., Mountford, T. Points of increase of the Brownian sheet. Probab Theory Relat Fields 108, 1–27 (1997). https://doi.org/10.1007/s004400050099
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DOI: https://doi.org/10.1007/s004400050099
- Mathematics Subject Classification: 60G60
- 60G15
- 60J65