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The goal of this paper is to approximate several kinds of {\it Mckean-Vlasov SDEs} with {\it irregular coefficients} via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme…

Probability · Mathematics 2019-06-06 Jianhai Bao , Xing Huang

We prove the well-posedness of solutions to McKean-Vlasov stochastic differential equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy measure is not required to be finite. The drift, diffusion and jump…

Probability · Mathematics 2020-10-20 Neelima , Sani Biswas , Chaman Kumar , Gonçalo dos Reis , Christoph Reisinger

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

We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…

Probability · Mathematics 2021-08-10 Oleg Butkovsky , Konstantinos Dareiotis , Máté Gerencsér

In this work, we study the convergence of the empirical measure of moderately interacting particle systems with singular interaction kernels. First, we prove quantitative convergence of the time marginals of the empirical measure of…

Probability · Mathematics 2021-12-22 Christian Olivera , Alexandre Richard , Milica Tomasevic

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

Probability · Mathematics 2025-09-01 Robert Alexander Crowell

The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…

Probability · Mathematics 2013-05-14 R. Mikulevicius , C. Zhang

We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…

Statistics Theory · Mathematics 2022-11-28 Louis Sharrock , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

Probability · Mathematics 2016-03-17 L Huang

We consider a novel McKean--Vlasov control problem with contagion through killing of particles and common noise. Each particle is killed at an exponential rate according to an intensity process that increases whenever the particle is…

Probability · Mathematics 2025-12-19 Ben Hambly , Philipp Jettkant

In this paper, our main aim is to investigate the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in(1/2, 1)$. After giving…

Numerical Analysis · Mathematics 2024-10-01 Shengrong Wang , Jie Xie , Li Tan

The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by L{\'e}vy processes on $\mathbb{R}^d$ having a finite moment of order $\beta \in [1,2]$ and under standard Lipschitz assumptions on the…

Probability · Mathematics 2025-04-24 Thomas Cavallazzi

In this paper, we present a generic methodology for the efficient numerical approximation of the density function of the McKean-Vlasov SDEs. The weak error analysis for the projected process motivates us to combine the iterative Multilevel…

Numerical Analysis · Mathematics 2019-09-27 Denis Belomestny , Lukasz Szpruch , Shuren Tan

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

A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…

Numerical Analysis · Mathematics 2022-05-04 Adam Andersson , Annika Lang , Andreas Petersson , Leander Schroer

We study a one-dimensional McKean-Vlasov stochastic differential equation (SDE) with a drift equal to a product of a distribution depending on the state of the process and a non-linear function depending pointwise on the law density of the…

Probability · Mathematics 2026-03-04 Luis Mario Chaparro Jaquez , Elena Issoglio , Jan Palczewski

This paper focuses on the numerical scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)\cup (1/2,1)$. The existence and uniqueness of the solutions to…

Numerical Analysis · Mathematics 2024-05-28 Shuaibin Gao , Qian Guo , Zhuoqi Liu , Chenggui Yuan

In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting super-linear growth…

Numerical Analysis · Mathematics 2023-06-21 Jianhai Bao , Christoph Reisinger , Panpan Ren , Wolfgang Stockinger

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

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