Erratum to “Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric -stable processes".
Estimates for the distribution of the first exit time of α-stable processes
The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
Exponential asymptotics for intersection local times of stable processes and random walks
Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces
We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...