## The Annals of Probability

### Multiple points of the Brownian sheet in critical dimensions

#### 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.

#### Article information

Source
Ann. Probab., Volume 43, Number 4 (2015), 1577-1593.

Dates
Revised: November 2013
First available in Project Euclid: 3 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1433341314

Digital Object Identifier
doi:10.1214/14-AOP912

Mathematical Reviews number (MathSciNet)
MR3353809

Zentralblatt MATH identifier
06457505

Subjects
Primary: 60G17: Sample path properties
Secondary: 60G15: Gaussian processes 60G60: Random fields

#### Citation

Dalang, Robert C.; Mueller, Carl. Multiple points of the Brownian sheet in critical dimensions. Ann. Probab. 43 (2015), no. 4, 1577--1593. doi:10.1214/14-AOP912. https://projecteuclid.org/euclid.aop/1433341314

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