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


  • Chow, Pao-Liu
  • Liu, Kai


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/

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