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We present a method to obtain sharp local propagation of chaos results for a system of N particles with a diffusion coefficient that it not constant and may depend of the empirical measure. This extends the recent works of Lacker [14] and…

Probability · Mathematics 2024-10-29 Jules Grass , Arnaud Guillin , Christophe Poquet

The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean-Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy…

Probability · Mathematics 2024-01-11 Xing Huang

We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…

Numerical Analysis · Mathematics 2018-02-13 Helmut Harbrecht , Marc Schmidlin

This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of…

Probability · Mathematics 2017-03-07 Jean-François Chassagneux , Dan Crisan , François Delarue

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

Probability · Mathematics 2021-10-05 Gunther Leobacher , Michaela Szölgyenyi , Stefan Thonhauser

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

We study a sequential system of interacting diffusions in which particle $i$ interacts only with its predecessors through the empirical measure $\mu_t^{i-1}$, yielding a directed, non-exchangeable mean-field approximation of a…

Probability · Mathematics 2026-02-03 Zhenfu Wang , Xianliang Zhao

The existence of random dynamical systems for McKean--Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying…

Probability · Mathematics 2025-07-04 Benjamin Gess , Rishabh S. Gvalani , Shanshan Hu

The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…

Probability · Mathematics 2022-12-09 Jun Gong , Huijie Qiao

We establish weak well-posedness for SDEs having discontinuous diffusion coefficients and general distributional drifts that may introduce local blow up effects. Our drifts satisfy minimal assumptions, i.e.\,we assume only that the Cauchy…

Probability · Mathematics 2025-12-01 D. Kinzebulatov , R. Vafadar

We revisit the variational characterization of diffusion as entropic gradient flux and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of…

Probability · Mathematics 2020-03-24 Ioannis Karatzas , Walter Schachermayer , Bertram Tschiderer

In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…

Probability · Mathematics 2025-08-05 Grigorios A. Pavliotis , Andrea Zanoni

We study the rate of propagation of chaos for a McKean--Vlasov equation with conditional expectation terms in the drift. We use a (regularized) Nadaraya--Watson estimator at a particle level to approximate the conditional expectations; we…

Probability · Mathematics 2025-07-31 Manuel Arnese

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…

Probability · Mathematics 2012-05-08 Marcel Nutz

The existence and uniqueness of stationary distributions and the exponential convergence in $L^p$-Wasserstein distance are derived for distribution dependent SDEs from associated decoupled equations. To establish the exponential…

Probability · Mathematics 2022-03-14 Shao-Qin Zhang

We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…

Disordered Systems and Neural Networks · Physics 2009-11-11 Sijmen Gerritsen , Gerrit E. W. Bauer

In this paper, we investigate a class of mean reflected McKean-Vlasov stochastic differential equation, which extends the equation proposed by \cite{briand2020particles} by allowing the solution's distribution to not only constrain its…

Probability · Mathematics 2024-11-21 Shaopeng Hong , Sheng Xiao

In this paper, the strong existence and uniqueness for a degenerate finite system of quantile-dependent McKean-Vlasov stochastic differential equations are obtained under a weak H\"{o}rmander condition. The approach relies on the apriori…

Probability · Mathematics 2021-03-15 Yaozhong Hu , Michael A. Kouritzin , Jiayu Zheng

In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical…

Classical Analysis and ODEs · Mathematics 2021-04-23 Paul-Eric Chaudru de Raynal , Noufel Frikha

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…

Probability · Mathematics 2013-03-14 Tomoyuki Ichiba , Mykhaylo Shkolnikov