Open Access
July 2015 Multiple points of the Brownian sheet in critical dimensions
Robert C. Dalang, Carl Mueller
Ann. Probab. 43(4): 1577-1593 (July 2015). DOI: 10.1214/14-AOP912


It is well known that an $N$-parameter $d$-dimensional Brownian sheet has no $k$-multiple points when $(k-1)d>2kN$, and does have such points when $(k-1)d<2kN$. We complete the study of the existence of $k$-multiple points by showing that in the critical cases where $(k-1)d=2kN$, there are a.s. no $k$-multiple points.


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Robert C. Dalang. Carl Mueller. "Multiple points of the Brownian sheet in critical dimensions." Ann. Probab. 43 (4) 1577 - 1593, July 2015.


Received: 1 February 2013; Revised: 1 November 2013; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 06457505
MathSciNet: MR3353809
Digital Object Identifier: 10.1214/14-AOP912

Primary: 60G17
Secondary: 60G15 , 60G60

Keywords: Brownian sheet , Girsanov’s theorem , multiple points

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 4 • July 2015
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