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

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.

We find a gap in the proof of lemma 3.2 about the Cauchy sequence