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Related papers: McKean-Vlasov SDEs in nonlinear filtering

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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 article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…

Methodology · Statistics 2012-09-05 Jamie Hall , Michael K. Pitt , Robert Kohn

We propose a micro-macro parallel-in-time Parareal method for scalar McKean-Vlasov stochastic differential equations (SDEs). In the algorithm, the fine Parareal propagator is a Monte Carlo simulation of an ensemble of particles, while an…

Numerical Analysis · Mathematics 2025-10-31 Ignace Bossuyt , Stefan Vandewalle , Giovanni Samaey

In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…

Statistics Theory · Mathematics 2025-06-10 Jan Szalankiewicz , Cristina Martinez-Torres , Wilhelm Stannat

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…

Numerical Analysis · Mathematics 2025-02-10 Jiamin Jian , Qingshuo Song , Xiaojie Wang , Zhongqiang Zhang , Yuying Zhao

"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random…

Computation · Statistics 2014-07-17 J. N. Corcoran , D. Jennings

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 propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full…

Methodology · Statistics 2022-11-28 Francesca R. Crucinio , Adam M. Johansen

Filtering algorithms are fundamental for inference on partially observed stochastic dynamic systems, since they provide access to the likelihood function and hence enable likelihood-based or Bayesian inference. A novel Poisson approximate…

Methodology · Statistics 2024-09-19 Yize Hao , Aaron A. Abkemeier , Edward L. Ionides

Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty by introducing adaptive biasing potentials to facilitate…

Numerical Analysis · Mathematics 2026-05-06 Liyao Lyu , Siyu Guo , Huan Lei

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 develop algorithms for computing expectations of the laws of models associated to stochastic differential equations (SDEs) driven by pure L\'evy processes. We consider filtering such processes and well as pricing of path dependent…

Computation · Statistics 2018-07-13 Ajay Jasra , Kody J. H. Law , Prince Peprah Osei

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications…

Methodology · Statistics 2026-02-03 Elsiddig Awadelkarim , Neil K. Chada , Ajay Jasra

We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to…

Numerical Analysis · Mathematics 2017-05-02 Abdul-Lateef Haji-Ali , Raul Tempone

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

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…

Neurons and Cognition · Quantitative Biology 2022-01-05 Anna Kutschireiter , Simone Carlo Surace , Henning Sprekeler , Jean-Pascal Pfister

The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo…

Computation · Statistics 2026-05-05 Jianfeng Lu , Yuliang Wang

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Machine Learning · Computer Science 2020-03-03 Xuan Su , Wee Sun Lee , Zhen Zhang

We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…

Probability · Mathematics 2025-11-05 Marc Hoffmann , Yating Liu

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

Numerical Analysis · Mathematics 2026-05-12 Ke Zhao , Ajay Jasra