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Related papers: McKean-Vlasov SDEs in nonlinear filtering

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Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an It\^o stochastic…

Computation · Statistics 2026-04-24 Utku Erdogan , Gabriel J. Lord , Joaquin Miguez

In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…

Computation · Statistics 2019-02-26 Matthieu Bulté , Jonas Latz , Elisabeth Ullmann

This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…

Methodology · Statistics 2008-04-29 Simo Särkkä , Tommi Sottinen

We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…

Probability · Mathematics 2021-04-13 Dan Crisan , Thomas G. Kurtz , Salvador Ortiz-Latorre

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

We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…

Statistics Theory · Mathematics 2016-11-15 Dionysios S. Kalogerias , Athina P. Petropulu

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

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

Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…

Machine Learning · Computer Science 2026-05-14 Wessel L. van Nierop , Nir Shlezinger , Ruud J. G. van Sloun

We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback…

Optimization and Control · Mathematics 2020-05-01 Martin A. Sehr , Robert R. Bitmead

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…

Computation · Statistics 2025-04-23 Ajay Jasra , Amin Wu

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the…

Computation · Statistics 2024-10-30 Juha Ala-Luhtala , Nick Whiteley , Kari Heine , Robert Piche

In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…

Methodology · Statistics 2018-05-15 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…

Artificial Intelligence · Computer Science 2013-01-07 Bhaskara Marthi , Hanna Pasula , Stuart Russell , Yuval Peres

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

Methodology · Statistics 2023-04-28 Konstantinos E. Tatsis , Vasilis K. Dertimanis , Eleni N. Chatzi

The work concerns about multiscale McKean-Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of…

Probability · Mathematics 2023-11-28 Huijie Qiao , Shengqing Zhu

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 introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…

Numerical Analysis · Mathematics 2025-01-03 Jingyuan Li , Wei Liu

We consider the discrete-time filtering problem in scenarios where the observation noise is degenerate or low. More precisely, one is given access to a discrete time observation sequence which at any time $k$ depends only on the state of an…

Computation · Statistics 2025-11-17 Abylay Zhumekenov , Alexandros Beskos , Dan Crisan , Ajay Jasra , Nikolas Kantas

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