English
Related papers

Related papers: Parameter Estimation for the McKean-Vlasov Stochas…

200 papers

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…

Statistics Theory · Mathematics 2023-06-26 Chiara Amorino , Akram Heidari , Vytautė Pilipauskaitė , Mark Podolskij

We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…

Statistics Theory · Mathematics 2026-02-25 Louis Sharrock , Nikolas Kantas , Grigorios A. Pavliotis

We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estimation of the finite-particle log-likelihood is not possible,…

Methodology · Statistics 2026-05-04 Louis Sharrock , Nikolas Kantas , Grigorios A. Pavliotis

The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct…

Probability · Mathematics 2020-06-03 Meiqi Liu , Huijie Qiao

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

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

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

We consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…

Statistics Theory · Mathematics 2021-03-16 Laetitia Della Maestra , Marc Hoffmann

We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$.…

Statistics Theory · Mathematics 2022-05-13 Laetitia Della Maestra , Marc Hoffmann

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of…

Machine Learning · Computer Science 2024-04-16 Haoming Yang , Ali Hasan , Yuting Ng , Vahid Tarokh

This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…

Statistics Theory · Mathematics 2022-06-28 Rentian Yao , Xiaohui Chen , Yun Yang

In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…

Methodology · Statistics 2022-04-12 Rohan Hore , Abhik Ghosh

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

Probability · Mathematics 2024-03-27 Kai Du , Yunzhang Li , Yuyang Ye

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

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

Probability · Mathematics 2025-09-30 Jie Xiang , Huijie Qiao

In this paper we study the problem of semiparametric estimation for a class of McKean-Vlasov stochastic differential equations. Our aim is to estimate the drift coefficient of a MV-SDE based on observations of the corresponding particle…

Statistics Theory · Mathematics 2021-07-02 Denis Belomestny , Vytautė Pilipauskaitė , Mark Podolskij

We study the local asymptotic normality (LAN) property for the likelihood function associated with discretely observed $d$-dimensional McKean-Vlasov stochastic differential equations over a fixed time interval. The model involves a joint…

Statistics Theory · Mathematics 2025-11-18 Akram Heidari , Mark Podolskij

In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…

Probability · Mathematics 2024-12-19 Yuewen Hou , Yun Li , Longjie Xie

Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…

Probability · Mathematics 2025-12-25 Yuanping Cui , Xiaoyue Li , Yi Liu , Fengyu Wang

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba
‹ Prev 1 2 3 10 Next ›