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This is a Quantitative Study study.

September 24, 2025Open Access

Strong and weak well-posedness of McKean-Vlasov SDEs driven by α-stable processes under unified condition

Key Points

Strong well-posedness is established for McKean-Vlasov SDEs with a Hölder kernel.
The strong condition coincides with the threshold for weak well-posedness of the processes.
The paper specifically focuses on $α$ in the range of (0,2) for the stable processes.
The presence of the Hölder (Besov) kernel is crucial for the findings on well-posedness.

Abstract

In this paper, we consider α (0, 2) and establish the strong well-posedness of McKean--Vlasov SDEs driven by an α-stable process with a Hölder (Besov) kernel K C^β, where β> 1-α. This condition coincides with the well-known threshold for the weak well-posedness.

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Cite This Study

Zimo Hao (Sun,) studied this question.

synapsesocial.com/papers/68d6e16f8b2b6861e4c400b6 https://doi.org/https://doi.org/10.48550/arxiv.2508.01895

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