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Support Theorem for Lévy-driven Stochastic Differential Equations

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  • Oleksii Kulyk

    (Wrocław University of Science and Technology)

Abstract

We provide a support theorem for the law of the solution to a stochastic differential equation (SDE) with jump noise. This theorem applies to quite general Lévy-driven SDEs and is illustrated by examples with rather degenerate jump noises, where the theorem leads to an informative description of the support.

Suggested Citation

  • Oleksii Kulyk, 2023. "Support Theorem for Lévy-driven Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1720-1742, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01223-8
    DOI: 10.1007/s10959-022-01223-8
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    References listed on IDEAS

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    1. Kulczycki, Tadeusz & Ryznar, Michał, 2020. "Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7185-7217.
    2. Kulik, Alexey M., 2009. "Exponential ergodicity of the solutions to SDE's with a jump noise," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 602-632, February.
    3. Simon, Thomas, 2000. "Support theorem for jump processes," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 1-30, September.
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