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 from Priola, Shirikyan, Xu and Zabczyk (2012). In the proof we use an idea of Maslowski and Seidler (1999).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-4,
author = {Anna Chojnowska-Michalik and Beniamin Goldys},
title = {Exponential ergodicity of semilinear equations driven by L\'evy processes in Hilbert spaces},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {59-72},
zbl = {1323.60082},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-4}
}
Anna Chojnowska-Michalik; Beniamin Goldys. Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces. Banach Center Publications, Tome 104 (2015) pp. 59-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-4/