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

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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 work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…

Quantum Physics · Physics 2024-06-19 Henrik Glavind Clausen , Pierre Rouchon , Rafal Wisniewski

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

Probability · Mathematics 2023-06-02 Wei Hong , Shihu Li , Wei Liu , Xiaobin Sun

In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…

Numerical Analysis · Mathematics 2025-04-10 Ajay Jasra , Abylay Zhumekenov

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…

Optimization and Control · Mathematics 2018-10-16 Simone Carlo Surace , Jean-Pascal Pfister

In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior…

Probability · Mathematics 2015-09-15 James Inglis , Denis Talay

This work develops a particle system addressing the approximation of McKean-Vlasov stochastic differential equations (SDEs). The novelty of the approach lies in involving low discrepancy sequences nontrivially in the construction of a…

Numerical Analysis · Mathematics 2024-09-17 Nadhir Ben Rached , Abdul-Lateef Haji-Ali , Raúl Tempone , Leon Wilkosz

Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and…

Probability · Mathematics 2025-04-02 Ke Song , Zimo Hao , Mingkun Ye

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

Statistics Theory · Mathematics 2013-10-30 Peter Bickel , David Choi , Xiangyu Chang , Hai Zhang

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

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 study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…

Statistics Theory · Mathematics 2025-09-19 Yuga Iguchi , Alexandros Beskos , Grigorios A. Pavliotis

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

Methodology · Statistics 2012-09-28 Soyoung Jeon , Richard L. Smith

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

Statistics Theory · Mathematics 2020-07-31 Fei Lu , Mauro Maggioni , Sui Tang

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

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…

Statistics Theory · Mathematics 2026-03-31 Chiara Amorino , Vytautė Pilipauskaitė

Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are…

Statistics Theory · Mathematics 2021-01-05 Vladislav Z. B. Tadic , Arnaud Doucet

In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…

Probability · Mathematics 2025-08-05 Grigorios A. Pavliotis , Andrea Zanoni

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…

Probability · Mathematics 2022-11-04 Yuanping Cui , Xiaoyue Li , Yi Liu , Chenggui Yuan

We present a proof showing that the weak error of a system of $n$ interacting stochastic particles approximating the solution of the McKean-Vlasov equation is $\mathcal O(n^{-1})$. Our proof is based on the Kolmogorov backward equation for…

Probability · Mathematics 2024-08-07 Abdul-Lateef Haji-Ali , Håkon Hoel , Raúl Tempone