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Related papers: Polynomial McKean-Vlasov SDEs

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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

In this paper, we present sufficient conditions and criteria to establish general large and moderate deviation principles for multivalued McKean-Vlasov stochastic differential equations (SDEs in short) by means of the weak convergence…

Probability · Mathematics 2025-07-10 Lingyan Cheng , Wei Liu , Huijie Qiao , Fengwu Zhu

This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…

Probability · Mathematics 2019-12-17 Martin Bauer , Thilo Meyer-Brandis

This paper is devoted to the problem of approximating non-linear Stochastic Partial Differential Equations (SPDEs) via interacting particle systems. In particular, we consider the Stochastic McKean-Vlasov equation, which is the…

Probability · Mathematics 2024-04-12 Letizia Angeli , Dan Crisan , Martin Kolodziejczyk , Michela Ottobre

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…

Probability · Mathematics 2007-07-19 Benjamin Jourdain , Sylvie Méléard , Wojbor Woyczynski

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

We produce uniform and decaying bounds in time for derivatives of the solution to the backwards Kolmogorov equation associated to a stochastic processes governed by a time dependent dynamics. These hold under assumptions over the…

Probability · Mathematics 2022-07-27 Maria Lefter , David Šiška , Łukasz Szpruch

We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…

Probability · Mathematics 2022-03-07 Lucio Galeati , Fabian A. Harang , Avi Mayorcas

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

McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…

Computation · Statistics 2026-01-21 Ning Ning , Amin Wu

In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data $(t,x)\in[0,T]\times R^d,$ which coefficients depend on both the solution $X^{t,x}_s$ but also its law. By…

Probability · Mathematics 2014-07-07 Rainer Buckdahn , Juan Li , Shige Peng , Catherine Rainer

We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the…

Probability · Mathematics 2025-06-16 Lukas Anzeletti , Lucio Galeati , Alexandre Richard , Etienne Tanré

We study a large class of McKean-Vlasov SDEs with drift and diffusion coefficient depending on the density of the solution's time marginal laws in a Nemytskii-type of way. A McKean-Vlasov SDE of this kind arises from the study of the…

Probability · Mathematics 2023-02-07 Sebastian Grube

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…

Probability · Mathematics 2014-09-17 Ying Hu , Yiming Jiang , Zhongmin Qian

We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric $\alpha$-stable L\'{e}vy process ($1/2<\alpha\leq1$), where the drift coefficient is H\"{o}lder continuous in space variable, while the noise coefficient…

Probability · Mathematics 2024-01-23 Chang-Song Deng , Xing Huang

We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the form $ dX_t = b(X_t) dt + \sigma(X_t)\circ d W_t, X_0=x_0\in\mathbb{R}^d, t\geq0,$ with a possibly singular drift $b\in…

Probability · Mathematics 2021-09-28 Chengcheng Ling , Sebastian Riedel , Michael Scheutzow

In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with…

Probability · Mathematics 2022-01-26 Xicheng Zhang

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 present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-established in the literature. While the…

Probability · Mathematics 2026-04-22 Alexander Kalinin , Thilo Meyer-Brandis , Annika Steibel

This work develops a particle system addressing the approximation of McKean-Vlasov stochastic differential equations (SDEs). The novelty of the approach lies in involving low discrepancy sequences nontrivially in the construction of a…

Numerical Analysis · Mathematics 2024-09-17 Nadhir Ben Rached , Abdul-Lateef Haji-Ali , Raúl Tempone , Leon Wilkosz