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Time regularity of solutions to linear equations with Lévy noise in infinite dimensions

Author

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  • Peszat, S.
  • Zabczyk, J.

Abstract

The existence of strong and weak càdlàg versions of a solution to a linear equation in a Hilbert space H, driven by a Lévy process taking values in a Hilbert space U↩H is established. The so-called cylindrical càdlàg property is investigated as well. A special emphasis is put on infinite systems of linear equations driven by independent Lévy processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:719-751
    DOI: 10.1016/j.spa.2012.10.012
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    Cited by:

    1. 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.
    2. Leahy, James-Michael & Mikulevičius, Remigijus, 2015. "On degenerate linear stochastic evolution equations driven by jump processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3748-3784.
    3. Yong Liu & Jianliang Zhai, 2016. "Time Regularity of Generalized Ornstein–Uhlenbeck Processes with Lévy Noises in Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 29(3), pages 843-866, September.

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