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On the regularity of weak solutions to space–time fractional stochastic heat equations

Author

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  • Zou, Guang-an
  • Lv, Guangying
  • Wu, Jiang-Lun

Abstract

This study is concerned with the space–time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of the Laplace transform and Mittag-Leffler function. Using the fractional calculus and stochastic analysis theory, we further prove the pathwise spatial–temporal regularity properties of weak solutions to this type of SPDEs in the framework of Bochner spaces.

Suggested Citation

  • Zou, Guang-an & Lv, Guangying & Wu, Jiang-Lun, 2018. "On the regularity of weak solutions to space–time fractional stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 84-89.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:84-89
    DOI: 10.1016/j.spl.2018.04.006
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    References listed on IDEAS

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    1. Mijena, Jebessa B. & Nane, Erkan, 2015. "Space–time fractional stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3301-3326.
    2. Chen, Zhen-Qing & Kim, Kyeong-Hun & Kim, Panki, 2015. "Fractional time stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1470-1499.
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