Multiple points of the Brownian sheet in critical dimensions

Dalang, Robert C. ^[1] ; Mueller, Carl ^[2]
1. [1] École Polytechnique
  
  École Polytechnique
  
  Arrondissement de Palaiseau, Francia
2. [2] University of Rochester
  
  University of Rochester
  
  City of Rochester, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 1577-1593
Idioma: inglés
DOI: 10.1214/14-AOP912
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Resumen
- 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.