Global attracting set,exponential stability and stability in distribution of SPDEs with jumps |
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Affiliation: | 1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, China;2. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China |
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Abstract: | A novel approach to the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Lévy noise is presented. Consequently, some new sufficient conditions ensuring the existence of the global attracting sets of mild solutions for the considered equations are established. As applications, some new criteria for the exponential stability in mean square of the considered equations is obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to stochastic delay partial differential equations with jumps under some weak conditions. Some known results are improved. Lastly, some examples are investigated to illustrate the theory. |
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Keywords: | Global attracting set Exponential stability Stability in distribution Stochastic functional partial differential equations Lévy process |
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