The LDP of McKean-Vlasov stochastic differential equations with H\"{o}lder continuous conditions and integrable conditions

Hao Wu; Junhao Hu; Chenggui Yuan

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arXiv · 2507.07368

The LDP of McKean-Vlasov stochastic differential equations with H\"{o}lder continuous conditions and integrable conditions

Hao Wu·Junhao Hu·Chenggui Yuan

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Abstract

In this paper, we first study the large deviation principle (LDP) for non-degenerate McKean-Vlasov stochastic differential equations (MVSDEs) with H\"{o}lder continuous drifts by using Zvonkin's transformation. When the drift only satisfies H\"{o}lder condition, the skeleton equation may have multiple solutions. Among these solutions, we find one that ensures the MVSDEs satisfy the LDP. Moreover, we introduce a new definition for the rate function that reduces to traditional rate function if the drift satisfies the Lipschitz condition. Secondly, we study the LDP for degenerate MVSDEs with H\"{o}lder continuous drifts.

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Hao Wu, Junhao Hu, Chenggui Yuan. 2025-07-10. The LDP of McKean-Vlasov stochastic differential equations with H\"{o}lder continuous conditions and integrable conditions. https://arxiv.org/abs/2507.07368

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