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One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to special cases in which the…

Optimization and Control · Mathematics 2023-09-20 Jiequn Han , Ruimeng Hu , Jihao Long

In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…

Probability · Mathematics 2022-06-07 Wei Hong , Shihu Li , Xiaobin Sun

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

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…

Probability · Mathematics 2022-11-04 Yuanping Cui , Xiaoyue Li , Yi Liu , Chenggui Yuan

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…

Statistics Theory · Mathematics 2017-10-16 Trisha Maitra , Sourabh Bhattacharya

This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of…

Probability · Mathematics 2025-08-01 Luca Bondi , Elena Issoglio , Francesco Russo

This paper focuses on the invariant measure of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN) whose coefficients depend on both the state and the measure. Using the existence of the unique solution of…

Probability · Mathematics 2025-09-23 Xing Chen , Xiaoyue Li , Chenggui Yuan

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient…

Probability · Mathematics 2018-05-07 Xing Huang , Feng-Yu Wang

By using the heat kernel parameter expansion with respect to the frozen SDEs, the intrinsic derivative is estimated for the law of Mckean-Vlasov SDEs with respect to the initial distribution. As an application, the total variation distance…

Probability · Mathematics 2020-07-01 Xing Huang , Feng-Yu Wang

We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the…

Probability · Mathematics 2025-02-27 Christa Cuchiero , Janka Möller

We study McKean--Vlasov Stochastic Differential Equations (MV-SDEs) whose drift and diffusion coefficients are of superlinear growth in \textit{all} their variables thus also superlinear in the measure component (the meaning is specified in…

Probability · Mathematics 2025-10-21 Simran Soni , Neelima , Chaman Kumar , Goncalo dos Reis

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…

Probability · Mathematics 2022-03-03 Rangel Baldasso , Alan Pereira , Guilherme Reis

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

Computation · Statistics 2016-05-19 Gavin A. Whitaker , Andrew Golightly , Richard J. Boys , Chris Sherlock

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…

Numerical Analysis · Mathematics 2025-10-21 Jingtao Zhu , Yuying Zhao , Siqing Gan

The main aim of this paper is to study the moderate deviation principle for McKean-Vlasov stochastic differential equations with multiple scales. Specifically, we are interested in the asymptotic estimates of the deviation processes…

Probability · Mathematics 2024-09-20 Wei Hong , Ge Li , Shihu Li

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and…

Probability · Mathematics 2024-02-29 Michele Coghi , Wolfgang Dreyer , Paul Gajewski , Clemens Guhlke , Peter Friz , Mario Maurelli

A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equation is studied. The existence and pathwise uniqueness of a…

Probability · Mathematics 2025-08-01 Daniela Morale , Leonardo Tarquini , Stefania Ugolini

The aim of this paper is to introduce several new particle representations for \textit{ergodic} McKean-Vlasov SDEs. We construct new algorithms by leveraging recent progress in weak convergence analysis of interacting particle system. We…

Probability · Mathematics 2019-01-18 H. AlRachid , Mireille Bossy , Cristiano Ricci , Lukasz Szpruch

In this paper, we consider McKean-Vlasov stochastic differential equations (MVSDEs) driven by L\'evy noise. By identifying the right equations satisfied by the solutions of the MVSDEs with shifted driving L\'evy noise, we build up a…

Probability · Mathematics 2020-11-18 Wei Liu , Yulin Song , Jianliang Zhai , Tusheng Zhang

This work concerns a type of coupled McKean-Vlasov stochastic differential equations (MVSDEs in short) with jumps. First, we prove superposition principles for these coupled MVSDEs with jumps and non-local space-distribution dependent…

Probability · Mathematics 2020-08-07 Huijie Qiao