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Moment boundedness of linear stochastic delay differential equations with distributed delay

Zhen Wang Hefei University of Technology Xiong Li Beijing Normal University Jinzhi Lei Tsinghua University

Classical Analysis and ODEs mathscidoc:1702.05003

Stochastic Processes and their Applications, 124, 486-612, 2014
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the rst moment stability is known to be identical to that of the corresponding deterministic delay differential equation. However, boundedness of the second moment is complicated and depends on the stochastic terms. In this paper, the characteristic function of the equation is obtained through techniques of the Laplace transform. From the characteristic equation, suf cient conditions for the second moment to be bounded or unbounded are proposed.
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@inproceedings{zhen2014moment,
  title={Moment boundedness of linear stochastic delay differential equations with distributed delay},
  author={Zhen Wang, Xiong Li, and Jinzhi Lei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210162002587810430},
  booktitle={Stochastic Processes and their Applications},
  volume={124},
  pages={486-612},
  year={2014},
}
Zhen Wang, Xiong Li, and Jinzhi Lei. Moment boundedness of linear stochastic delay differential equations with distributed delay. 2014. Vol. 124. In Stochastic Processes and their Applications. pp.486-612. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210162002587810430.
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