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The work concerns the stability for a type of multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients. First, we prove the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equations with non-Lipschitz coefficients. Then, we extend the classical It^{o}s formula from SDEs to multivalued McKean-Vlasov SDEs. Next, the exponential stability of second moments, the exponentially 2-ultimate boundedness and the almost surely asymptotic stability for their solutions in terms of a Lyapunov function are shown.
The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense
By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular reflecting
In this paper, utilizing Wangs Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for distribution dependent SDEs with integrable drift is investigated. In addition, using a trick of decoupled method, some regul
The following type exponential convergence is proved for (non-degenerate or degenerate) McKean-Vlasov SDEs: $$W_2(mu_t,mu_infty)^2 +{rm Ent}(mu_t|mu_infty)le c {rm e}^{-lambda t} minbig{W_2(mu_0, mu_infty)^2,{rm Ent}(mu_0|mu_infty)big}, tge 1,$$ whe
Regularity estimates and Bismut formula of $L^k$ ($kge 1$) intrinsic-Lions derivative are presented for singular McKean-Vlasov SDEs, where the noise coefficient belongs to a local Sobolev space, and the drift contains a locally integrable time-space