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We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for…

Probability · Mathematics 2024-08-21 Alexander Kalinin , Thilo Meyer-Brandis , Frank Proske

In this article, we investigate three classes of equations: the McKean-Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean-Vlasov stochastic variational inequality (MVSVI),…

Probability · Mathematics 2024-01-31 Ning Ning , Jing Wu , Jinwei Zheng

By using a classical truncated argument and introducing the local Wasserstein distance, the global existence and uniqueness are proved for the distribution dependent SDEs with local Lipschitz coefficients. Due to the measure dependence, the…

Probability · Mathematics 2021-03-25 Shan-Shan Hu

We consider multidimensional SDEs with singular drift $b$ and Sobolev diffusion coefficients $\sigma$, satisfying Krylov--R\"ockner type assumptions. We prove several stability estimates, comparing solutions driven by different…

Probability · Mathematics 2022-08-09 Lucio Galeati , Chengcheng Ling

We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular and unbounded coefficients. Under mild local structural…

Probability · Mathematics 2026-04-02 Pengcheng Xia , Longjie Xie , Xicheng Zhang

Let P2(Rd) be the space of probability measures on Rd with finite second moment. The path independence of additive functionals of McKean-Vlasov SDEs is characterized by PDEs on the product space Rd*P2(Rd) equipped with the usual derivative…

Probability · Mathematics 2018-06-07 Panpan Ren , Feng-Yu Wang

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong…

Probability · Mathematics 2024-11-05 Alexander Kalinin , Thilo Meyer-Brandis , Frank Proske

We consider various approximation properties for systems driven by a Mc Kean-Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations…

Probability · Mathematics 2019-10-01 Mohamed Amine Mezerdi , Khaled Bahlali , Nabil Khelfallah , Brahim Mezerdi

In this paper we prove a new strong uniqueness result and a weak existence result for possibly {\it degenerate} multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples…

Probability · Mathematics 2018-05-16 Zhen Wang , Xicheng Zhang

Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the…

Probability · Mathematics 2019-11-12 Yongqiang Suo , Chenggui Yuan

New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equations are established under relaxed regularity conditions. Weak existence is a variation of Krylov's weak existence for…

Probability · Mathematics 2024-05-29 Yuliya S. Mishura , Alexander Yu. Veretennikov

Being concerned with ergodicity of McKean--Vlasov SDEs, we establish a general result on exponential ergodicity in the $L^1$-Wasserstein distance. The result is successfully applied to non-degenerate and multiplicative Brownian motion…

Probability · Mathematics 2025-01-23 Xing Huang , Huaiqian Li , Liying Mu

In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…

Probability · Mathematics 2009-08-18 Xicheng Zhang

In this short note, we establish Malliavin differentiability of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts satisfying both a locally Lipschitz and a one-sided Lipschitz assumption, and where the diffusion…

Probability · Mathematics 2025-05-09 Goncalo dos Reis , Zac Wilde

In this paper, the existence and uniqueness of strong solutions to distribution dependent neutral SFDEs are proved. We give the conditions such that the order preservation of these equations holds. Moreover, we show these conditions are…

Probability · Mathematics 2019-04-12 Xing Huang , Chenggui Yuan

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

Probability · Mathematics 2025-01-17 Wei Sun , Ethan Wong

By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…

Probability · Mathematics 2024-12-10 Xing Huang , Xiaochen Ma

In this paper, by utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with integrable drift is investigated. In addition, using the decoupled method, some…

Probability · Mathematics 2021-10-19 Xing Huang , Shen Wang , Fen-Fen Yang

By the approximation method introduced in \cite{FYW}, the existence and uniqueness are proved for a class of distribution-dependent stochastic functional differential equations (DDSFDEs). Moreover, combining the Harnack and shift-Harnack…

Probability · Mathematics 2018-01-26 Xing Huang

We introduce a framework for stochastic differential equations (SDEs) with interaction on compact, connected, $d$-dimensional manifolds. For SDEs whose drift and diffusion coefficients may depend on both the state variable and the empirical…

Probability · Mathematics 2026-01-27 Andrey Dorogovtsev , Alexander Weiß