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

Alexander Bendikov, Laurent Saloff-Coste

• 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 < ∞.