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Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise

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  • Kumar, Vivek

Abstract

In this work, we study the stochastic heat equation with Caputo derivative perturbed by a class of noises that include Gaussian noises and non-Gaussian noises. We have deduced the existence, uniqueness and pathwise spatial–temporal regularity properties of mild solutions to the corresponding non-linear time-fractional stochastic heat type equation.

Suggested Citation

  • Kumar, Vivek, 2022. "Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000104
    DOI: 10.1016/j.spl.2022.109381
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    References listed on IDEAS

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    1. Wei Liu & Kuanhou Tian & Mohammud Foondun, 2017. "On Some Properties of a Class of Fractional Stochastic Heat Equations," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1310-1333, December.
    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.
    3. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
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