On the sample paths of Brownian motions on compact infinite dimensional groups

• Alexander Bendikov ^[1] ; Laurent Saloff-Coste ^[1]
  1. [1] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1464-1493
• Idioma: inglés
• DOI: 10.1214/aop/1055425787
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• Resumen

  • We study the regularity of the sample paths of certain Brownian motions on the infinite dimensional torus T∞ and other compact connected groups in terms of the associated intrinsic distance. For each λ∈(0,1), we give examples where the intrinsic distance d is continuous and defines the topology of T∞ and where the sample paths satisfy 0 < lim inft\ra0d(X0,Xt)t(1−λ)/2 ≤ lim supt\ra0d(X0,Xt)t(1−λ)/2 < ∞ and 0 < limε→0sup0 < t < s < 1t−s ≤ εd(Xs,Xt)(t−s)(1−λ)/2 < ∞.