Abstract
A criteria for the algebraic convergence rate of diffusion semigroups on manifolds with respect to some Lipschitz norms in L2-sense is presented by using a Lyapunov condition. As application, we apply it to some diffusion processes with heavy tailed invariant distributions. This result is further extended to the reflecting diffusion processes on manifolds with non-convex boundary by using a conformal change of the metric.
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