Multiple points of the Brownian sheet in critical dimensions

Robert C. Dalang; Carl Mueller

doi:10.1214/14-AOP912

Multiple points of the Brownian sheet in critical dimensions

Probability 2015-09-10 v3

Authors: 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.

Keywords

Brownian sheet multiple points critical dimensions almost sure existence k-multiple points N-parameter

Cite

@article{arxiv.1303.0403,
  title  = {Multiple points of the Brownian sheet in critical dimensions},
  author = {Robert C. Dalang and Carl Mueller},
  journal= {arXiv preprint arXiv:1303.0403},
  year   = {2015}
}

Comments

Published at http://dx.doi.org/10.1214/14-AOP912 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Multiple points of the Brownian sheet in critical dimensions

Abstract

Keywords

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