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Moment boundedness of linear stochastic delay differential equations with distributed delay

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  • Wang, Zhen
  • Li, Xiong
  • Lei, Jinzhi

Abstract

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 first 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, sufficient conditions for the second moment to be bounded or unbounded are proposed.

Suggested Citation

  • Wang, Zhen & Li, Xiong & Lei, Jinzhi, 2014. "Moment boundedness of linear stochastic delay differential equations with distributed delay," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 586-612.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:586-612
    DOI: 10.1016/j.spa.2013.09.002
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
    2. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
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