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Hyperbolic Type Stochastic Evolution Equations with Lévy Noise

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Abstract

The existence and uniqueness of the solutions for a class of hyperbolic type stochastic evolution equations driven by some non-Gaussian Lévy processes are obtained. Moreover, an energy equality for the solutions of the equations is established. As examples, theses results are applied to a couple of stochastic wave type equations with jumps.

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Acknowledgements

We would like to thank Professor Jingqiao Duan for helpful discussions and comments. The research of the authors is supported by China NSF Grant No. 10901065, 11271295.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073, China

    Hongbo Fu & Li Wan

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jicheng Liu

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  1. Hongbo Fu
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  2. Jicheng Liu
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  3. Li Wan
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Correspondence to Hongbo Fu.

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Fu, H., Liu, J. & Wan, L. Hyperbolic Type Stochastic Evolution Equations with Lévy Noise. Acta Appl Math 125, 193–208 (2013). https://doi.org/10.1007/s10440-012-9787-y

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  • DOI: https://doi.org/10.1007/s10440-012-9787-y

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