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

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This is a Quantitative Study study.

Zimo Hao

doi:10.48550/arxiv.2508.01895

August 3, 2025Open Access

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

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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.

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Implication

This paper establishes strong and weak well-posedness for McKean-Vlasov SDEs driven by $α$-stable processes, indicating a unified condition.

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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Zimo Hao (2025) studied this question.

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

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

Key Points

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Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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