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

Anna Chonowska-Michalik; Beniamin Goldys

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arXiv · 1404.3323

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

Anna Chonowska-Michalik·Beniamin Goldys

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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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BibTeX RIS

Anna Chonowska-Michalik, Beniamin Goldys. 2014-04-12. Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces. https://arxiv.org/abs/1404.3323

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