数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 731-746.doi: 10.1007/s10473-019-0307-2

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ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LEVY PROCESS

江一鸣1, 王苏鑫2, 王兴春3   

  1. 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
    2. College of Science, Civil Aviation University of China, Tianjin 300300, China;
    3. School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China
  • 收稿日期:2018-06-30 修回日期:2018-11-12 出版日期:2019-06-25 发布日期:2019-06-27
  • 通讯作者: Suxin WANG E-mail:wangsuxinnk@163.com
  • 作者简介:Yiming JIANG,E-mail:ymjiangnk@nankai.edu.cn;Xingchun WANG,E-mail:xchwangnk@aliyun.com
  • 基金资助:
    Y. Jiang is supported by National Natural Science Foundation of China (11571190) and the Fundamental Research Funds for the Central Universities; S. Wang is supported by the China Scholarship Council (201807315008), National Natural Science Foundation of China (11501565), and the Youth Project of Humanities and Social Sciences of Ministry of Education (19YJCZH251); and X. Wang is supported by National Natural Science Foundation of China (11701084 and 11671084).

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LEVY PROCESS

Yiming JIANG1, Suxin WANG2, Xingchun WANG3   

  1. 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
    2. College of Science, Civil Aviation University of China, Tianjin 300300, China;
    3. School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China
  • Received:2018-06-30 Revised:2018-11-12 Online:2019-06-25 Published:2019-06-27
  • Contact: Suxin WANG E-mail:wangsuxinnk@163.com
  • Supported by:
    Y. Jiang is supported by National Natural Science Foundation of China (11571190) and the Fundamental Research Funds for the Central Universities; S. Wang is supported by the China Scholarship Council (201807315008), National Natural Science Foundation of China (11501565), and the Youth Project of Humanities and Social Sciences of Ministry of Education (19YJCZH251); and X. Wang is supported by National Natural Science Foundation of China (11701084 and 11671084).

摘要: In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

关键词: Stochastic wave equations, non-Gaussian Lévy processes, exponential stability, second moment stability

Abstract: In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

Key words: Stochastic wave equations, non-Gaussian Lévy processes, exponential stability, second moment stability

中图分类号: 

  • 60H15