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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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    References listed on IDEAS

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    1. Viens, Frederi G., 2009. "Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3671-3698, October.
    2. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    3. Bo Martin Bibby, 2001. "Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 99-112.
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