Open Access
January 2002 Eccentric Behaviors of the Brownian Sheet Along Lines
Robert C. Dalang, T. Mountford
Ann. Probab. 30(1): 293-322 (January 2002). DOI: 10.1214/aop/1020107769


Distinct excursion intervals of a Brownian motion (that correspond to a fixed level) have no common endpoints. What is the situation for distinct excursion sets of a Brownian sheet? These sets are termed Brownian bubbles in the literature, and this paper examines how bubbles from fixed or random levels come into contact with each other, by examining whether or not the Brownian sheet restricted to a specific type of curve can have a point of increase. At random levels, we show that points of increase can occur along horizontal lines, while at fixed levels, such a point of increase can occur at the corner of a broken line segment with a right-angle. In addition, the Hausdorff dimension of the set of points with this last property is shown to be 1/2 a.s.


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Robert C. Dalang. T. Mountford. "Eccentric Behaviors of the Brownian Sheet Along Lines." Ann. Probab. 30 (1) 293 - 322, January 2002.


Published: January 2002
First available in Project Euclid: 29 April 2002

zbMATH: 1019.60047
Digital Object Identifier: 10.1214/aop/1020107769

Primary: 60G60
Secondary: 60G15 , 60G17

Keywords: Brownian sheet , Level sets , points of increase

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 1 • January 2002
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