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Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

Author

Listed:
  • Tomasz Kosmala

    (King’s College London)

  • Markus Riedle

    (King’s College London)

Abstract

We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$ p ∈ [ 1 , 2 ] . The space of integrands consists of p-summing operators between Banach spaces of martingale type p. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

Suggested Citation

  • Tomasz Kosmala & Markus Riedle, 2021. "Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators," Journal of Theoretical Probability, Springer, vol. 34(1), pages 477-497, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00978-x
    DOI: 10.1007/s10959-019-00978-x
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    References listed on IDEAS

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    1. Carsten Chong, 2017. "Lévy-driven Volterra Equations in Space and Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1014-1058, September.
    2. Chong, Carsten, 2017. "Stochastic PDEs with heavy-tailed noise," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2262-2280.
    3. Peszat, S. & Zabczyk, J., 2013. "Time regularity of solutions to linear equations with Lévy noise in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 719-751.
    Full references (including those not matched with items on IDEAS)

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