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arXiv · 1303.0403

Multiple points of the Brownian sheet in critical dimensions

Robert C. Dalang·Carl Mueller
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Abstract

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. 2015-09-09. Multiple points of the Brownian sheet in critical dimensions. https://doi.org/10.1214/14-aop912

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