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Probability solution for time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measure

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  • Xu, Siyan
  • Zhao, Huiyan

Abstract

In this paper, we consider a class of generalized time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measures, where time–space-dependent Lévy measures contain stable-like Lévy measures as special examples. After that, probability solutions are constructed for such Fokker–Planck–Kolmogorov equations based on the correspondence between the time–space-dependent Lévy measure and its related SDE.

Suggested Citation

  • Xu, Siyan & Zhao, Huiyan, 2025. "Probability solution for time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measure," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000720
    DOI: 10.1016/j.spl.2025.110427
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    References listed on IDEAS

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    1. Marjorie Hahn & Kei Kobayashi & Sabir Umarov, 2012. "SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations," Journal of Theoretical Probability, Springer, vol. 25(1), pages 262-279, March.
    2. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    3. Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
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