Well-Posedness for McKean-Vlasov SDEs with Distribution Dependent Stable Noises

2023/06/19 by Deng, Chang-Song, Huang, Xing
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.10970

Abstract

The well-posedness is established for McKean-Vlasov SDEs driven by α-stable noises (1<α<2). In this model, the drift is Hölder continuous in space variable and Lipschitz continuous in distribution variable with respect to the sum of Wasserstein and weighted variation distances, while the noise coefficient satisfies the Lipschitz condition in distribution variable with respect to the sum of two Wasserstein distances. The main tool relies on Zvonkin's transform, a time-change technique and a two-step fixed point argument.

Related

• Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises
• McKean-Vlasov SDEs with Singular Coefficients and Distribution Dependent Noise: Well-posedness and Regularity
• Singular McKean-Vlasov (Reflecting) SDEs with Distribution Dependent Noise
• Well-posedness of McKean-Vlasov SDEs with density-dependent drift
• Strong and weak well-posedness of McKean-Vlasov SDEs driven by α-stable processes under unified condition