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

Anna Chojnowska-Michalik; Beniamin Goldys

Banach Center Publications (2015)

- Volume: 105, Issue: 1, page 59-72
- ISSN: 0137-6934

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topAnna Chojnowska-Michalik, and Beniamin Goldys. "Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces." Banach Center Publications 105.1 (2015): 59-72. <http://eudml.org/doc/281713>.

@article{AnnaChojnowska2015,

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 from Priola, Shirikyan, Xu and Zabczyk (2012). In the proof we use an idea of Maslowski and Seidler (1999).},

author = {Anna Chojnowska-Michalik, Beniamin Goldys},

journal = {Banach Center Publications},

keywords = {semilinear stochastic evolution equations; Lévy noise; exponential ergodicity; invariant measure; -stable cylindrical noise; Wiener process},

language = {eng},

number = {1},

pages = {59-72},

title = {Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces},

url = {http://eudml.org/doc/281713},

volume = {105},

year = {2015},

}

TY - JOUR

AU - Anna Chojnowska-Michalik

AU - Beniamin Goldys

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

JO - Banach Center Publications

PY - 2015

VL - 105

IS - 1

SP - 59

EP - 72

AB - 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).

LA - eng

KW - semilinear stochastic evolution equations; Lévy noise; exponential ergodicity; invariant measure; -stable cylindrical noise; Wiener process

UR - http://eudml.org/doc/281713

ER -

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