Ornstein–Uhlenbeck semi-groups on stratified groups

摘要

We consider, in the setting of stratified groups G, two analogues of the Ornstein–Uhlenbeck semi-group, namely Markovian diffusion semi-groups acting on Lq(pdr ), whose invariant density p is a heat kernel at time 1 on G. Both generators have the same “carre du champ”. The first semi-group is symmetric on L2(pdr ), with generatori=1 Xi Xi, where (Xi )n i=1 is a basis of the first layer of the Lie algebra of G. The second one is compact on Lq(pdr ), 1