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

• Autorzy: Anna Chojnowska-Michalik , Beniamin Goldys
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 60G51: Processes with independent increments; L\'evy processes
• 60H15: Stochastic partial differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 105
• Numer: 1
• Strony: 59-72

Daty

wydano

2015

Twórcy

autor

Anna Chojnowska-Michalik

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

autor

Beniamin Goldys

• School of Mathematics and Statistics, The University of Sydney, Sydney 2006, Australia

Identyfikatory

DOI

10.4064/bc105-0-4