The LDP of McKean-Vlasov stochastic differential equations with Hölder continuous conditions and integrable conditions

2025/07/10 by Wu Hao, Junhao Hu, Wu, Hao +3
Computer Science · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2507.07368

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first study the large deviation principle (LDP) for non-degenerate McKean-Vlasov stochastic differential equations (MVSDEs) with Hölder continuous drifts by using Zvonkin's transformation. When the drift only satisfies Hölder 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 Hölder continuous drifts.

Citations

• Central Limit Type Theorem and Large Deviation Principle for Multi-Scale McKean-Vlasov SDEs
• Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations
• Moderate Deviation Principles for Unbounded Additive Functionals of Distribution Dependent SDEs
• Large Deviations Principle for SDEs with Dini Continuous Drifts
• Well-posedness of distribution dependent SDEs with singular drifts
• Distribution-Dependent SDEs for Landau Type Equations
• Distribution dependent SDEs for Landau type equations
• Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder drift
• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• Gradient Estimates and Applications for SDEs in Hilbert Space with Multiplicative Noise and Dini Continuous Drift
• Uniqueness Theorems for Ordinary Differential Equations with Hölder Continuity

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• General large deviations and functional iterated logarithm law for multivalued McKean-Vlasov stochastic differential equations
• CLT and MDP for McKean-Vlasov SDEs