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Positivity and explosion in mean Lp-norm of stochastic functional parabolic equations of retarded type

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  • Chow, Pao-Liu
  • Liu, Kai

Abstract

This work is concerned with a class of semilinear stochastic functional parabolic differential equations of retarded type. We first establish conditions to ensure the existence of a unique non-negative solution of the stochastic delay partial differential equation under investigation. Subsequently, the problem of explosive or blow-up solutions in mean Lp-norm sense, p≥1, in a finite time to the stochastic system is considered. Several examples are given to illustrate the theory established in the work.

Suggested Citation

  • Chow, Pao-Liu & Liu, Kai, 2012. "Positivity and explosion in mean Lp-norm of stochastic functional parabolic equations of retarded type," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1709-1729.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1709-1729
    DOI: 10.1016/j.spa.2012.01.012
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    Cited by:

    1. Lv, Guangying & Wei, Jinlong, 2020. "Blowup solutions for stochastic parabolic equations," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Jianhai Bao & Chenggui Yuan, 2016. "Blow-up for Stochastic Reaction-Diffusion Equations with Jumps," Journal of Theoretical Probability, Springer, vol. 29(2), pages 617-631, June.

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