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This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the…

Statistics Theory · Mathematics 2024-11-01 Chiara Amorino , Denis Belomestny , Vytautė Pilipauskaitė , Mark Podolskij , Shi-Yuan Zhou

In this paper, we introduce adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz…

Numerical Analysis · Mathematics 2021-11-02 Christoph Reisinger , Wolfgang Stockinger

For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly to the exact solution. Recently, an…

Numerical Analysis · Mathematics 2014-08-26 Xiaojie Wang , Siqing Gan

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

This paper presents a strong convergence rate analysis of general discretization approximations for McKean-Vlasov SDEs with super-linear growth coefficients over infinite time horizon. Under some specified non-globally Lipschitz conditions,…

Numerical Analysis · Mathematics 2025-09-12 Taiyuan Liu , Yaozhong Hu , Siqing Gan

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

This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical…

Probability · Mathematics 2026-04-17 Zhen Wang , Mingyan Wu

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

We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, these systems are described by a McKean-Vlasov process - a…

Numerical Analysis · Mathematics 2015-08-11 L. F. Ricketson

We develop and analyze a general class of Euler-type numerical schemes for Levy-driven McKean-Vlasov stochastic differential equations (SDEs), where the drift, diffusion and jump coefficients grow super-linearly in the state variable. These…

Numerical Analysis · Mathematics 2025-09-12 Jingtao Zhu , Yuying Zhao , Siqing Gan

This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…

Numerical Analysis · Mathematics 2021-12-28 Shuaibin Gao , Junhao Hu , Jie He , Qian Guo

We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…

Numerical Analysis · Mathematics 2018-08-15 Claudine Leonhard , Andreas Rößler

We consider a class of L\'evy-driven stochastic differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the coefficient is bounded, affine in the state variable, and only measurable…

Probability · Mathematics 2018-12-13 Ankush Agarwal , Stefano Pagliarani

We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems.…

Machine Learning · Statistics 2025-10-15 Joanna Marks , Tim Y. J. Wang , O. Deniz Akyildiz

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

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov

In this paper, a multilevel Monte Carlo theta EM scheme is provided for stochastic differential delay equations with small noise. Under a global Lipschitz condition, the variance of two coupled paths is derived. Then, the global Lipschitz…

Numerical Analysis · Mathematics 2019-04-17 Li Tan , Chenggui Yuan

In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…

Probability · Mathematics 2025-07-11 Manh Hong Duong , Grigorios A. Pavliotis , Julian Tugaut

In this paper, we study well-posedness of random periodic solutions of stochastic differential equations (SDEs) of McKean-Vlasov type driven by a two-sided Brownian motion, where the random periodic behaviour is characterised by the…

Probability · Mathematics 2024-12-05 Jianhai Bao , Goncalo Dos Reis , Yue Wu

In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…

Statistics Theory · Mathematics 2017-07-28 Ajay Jasra , Kengo Kamatani , Hiroki Masuda