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We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves…

Machine Learning · Computer Science 2025-12-18 Felipe J. P. Antunes , Yuri F. Saporito , Sebastian Jaimungal

We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

We present two fully probabilistic Euler schemes, one explicit and one implicit, for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of super-linear growth and random initial condition. We provide a…

Probability · Mathematics 2020-12-29 G. dos Reis , S. Engelhardt , G. Smith

We establish a Freidlin-Wentzell type large deviation principle (LDP) for a class of stochastic partial differential equations with locally monotone coefficients driven by L\'evy noise. Our results essentially improve a recent work on this…

Probability · Mathematics 2024-01-23 Weina Wu , Jianliang Zhai , Jiahui Zhu

We study a class of McKean-Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and…

Probability · Mathematics 2021-04-13 Zhongmin Qian , Yuhan Yao

We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Levy noise. We use general large deviations theorems of Varadhan and Bryc, viscosity solutions of integro-partial…

Probability · Mathematics 2010-03-09 Andrzej Swiech , Jerzy Zabczyk

In this article, we prove the existence of weak solutions as well as the existence and uniqueness of strong solutions for McKean-Vlasov multivalued stochastic differential equations with oblique subgradients (MVMSDEswOS, for short) by means…

Probability · Mathematics 2022-07-26 Hao Wu , Junhao Hu , Chenggui Yuan

In this paper, we study well-posedness of McKean-Vlasov stochastic differential equations (SDE) whose drift depends pointwisely on marginal density and satisfies a local integrability condition in time-space variables. The drift and noise…

Probability · Mathematics 2025-11-20 Anh-Dung Le , Stéphane Villeneuve

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

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 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 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 introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…

Numerical Analysis · Mathematics 2025-01-03 Jingyuan Li , Wei Liu

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

This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…

Probability · Mathematics 2025-01-28 Jiaohui Xu , Tomás Caraballo , José Valero

This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition…

Probability · Mathematics 2020-06-29 William R. P. Hammersley , David Šiška , Łukasz Szpruch

Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems…

Optimization and Control · Mathematics 2025-11-13 Ruimeng Hu , Botao Jin , Mathieu Laurière , Jiacheng Zhang

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

In this paper, we estimate the variance of two coupled paths derived with the Multilevel Monte Carlo method combined with the Euler Maruyama discretization scheme for the simulation of McKean-Vlasov stochastic differential equations with…

Probability · Mathematics 2023-10-03 Ulises Botija-Munoz , Chenggui Yuan

We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…

Probability · Mathematics 2007-05-23 Alexey Kulik