Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces

2014/04/12 by Chonowska-Michalik, Anna, Goldys, Beniamin
#60G51 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1404.3323

Abstract

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 operator. In particular, in the equation with diagonal pure α-stable cylindrical noise introduced by Priola and Zabczyk we generalize results in [12]. In the proof we use an idea of Maslowski and Seidler from [10].

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