English
Related papers

Related papers: Error Analysis of Time-Discrete Random Batch Metho…

200 papers

Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…

Analysis of PDEs · Mathematics 2024-10-21 Nathalie Ayi , Nastassia Pouradier Duteil , David Poyato

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

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Optimization and Control · Mathematics 2019-03-15 Melike Sirlanci , Susan E. Luczak , I. Gary Rosen

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…

Numerical Analysis · Mathematics 2021-06-08 Hao Luo , Xiaoping Xie

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

We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness…

Probability · Mathematics 2024-09-12 Julien Claisse , Jiazhi Kang , Xiaolu Tan

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…

Computation · Statistics 2023-09-26 Pierre Del Moral , Shulan Hu , Ajay Jasra , Hamza Ruzayqat , Xinyu Wang

We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…

Probability · Mathematics 2011-10-25 A. Manita , V. Shcherbakov

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

Probability · Mathematics 2023-07-21 Anirudh Sridhar , Soummya Kar

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…

Probability · Mathematics 2025-10-07 Louis-Pierre Chaintron , Antoine Diez

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…

Artificial Intelligence · Computer Science 2012-05-14 Ido Cohn , Tal El-Hay , Nir Friedman , Raz Kupferman

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…

Probability · Mathematics 2020-11-24 Xavier Erny , Eva Löcherbach , Dasha Loukianova

Sources of variability in experimentally derived data include measurement error in addition to the physical phenomena of interest. This measurement error is a combination of systematic components, originating from the measuring instrument,…

Machine Learning · Statistics 2018-01-10 Uri Shaham , Kelly P. Stanton , Jun Zhao , Huamin Li , Khadir Raddassi , Ruth Montgomery , Yuval Kluger

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

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…

Optimization and Control · Mathematics 2024-09-17 Alexander Pichugin , Maksim Pechin , Aleksandr Beznosikov , Vasilii Novitskii , Alexander Gasnikov

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…

Computation · Statistics 2023-11-17 Miguel Alvarez , Ajay Jasra , Hamza Ruzayqat

The random batch Ewald (RBE) is an efficient and accurate method for molecular dynamics (MD) simulations of physical systems at the nano-/micro- scale. The method shows great potential to solve the computational bottleneck of long-range…

Computational Physics · Physics 2022-05-31 Jiuyang Liang , Zhenli Xu , Yue Zhao

Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…

Analysis of PDEs · Mathematics 2025-07-30 Sebastian Throm

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

Optimization and Control · Mathematics 2026-03-31 José A. Carrillo , Shi Jin , Haoyu Zhang , Yuhua Zhu

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…

Probability · Mathematics 2009-02-16 Charles Bordenave , David McDonald , Alexandre Proutiere