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Stochastic evolution equations driven by cylindrical stable noise

Author

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  • Kosmala, Tomasz
  • Riedle, Markus

Abstract

We prove existence and uniqueness of a mild solution of a stochastic evolution equation driven by a standard α-stable cylindrical Lévy process defined on a Hilbert space for α∈(1,2). The coefficients are assumed to map between certain domains of fractional powers of the generator present in the equation. The solution is constructed as a weak limit of the Picard iteration using tightness arguments. Existence of strong solution is obtained by a general version of the Yamada–Watanabe theorem.

Suggested Citation

  • Kosmala, Tomasz & Riedle, Markus, 2022. "Stochastic evolution equations driven by cylindrical stable noise," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 278-307.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:278-307
    DOI: 10.1016/j.spa.2022.03.014
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    References listed on IDEAS

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    1. Chong, Carsten, 2017. "Stochastic PDEs with heavy-tailed noise," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2262-2280.
    2. Raluca M. Balan, 2014. "SPDEs with -Stable Lévy Noise: A Random Field Approach," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-22, February.
    3. Xiong, Jie & Yang, Xu, 2019. "Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2681-2722.
    4. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
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