On the stability and the uniform propagation of chaos properties of ensemble Kalman-Bucy filters

DOI10.1214/17-AAP1317zbMath1391.60082arXiv1605.09329OpenAlexW2964163851WikidataQ129994872 ScholiaQ129994872MaRDI QIDQ1650090

Julian Tugaut, Pierre Del Moral

Publication date: 29 June 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09329

zbMATH Keywords

Riccati equationsinteracting particle systemssequential Monte Carlo methodsensemble Kalman filterKalman-Bucy filternonlinear Markov processesrandom covariance matricesill-conditioned systemsmean-field particle models

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Inference from stochastic processes and prediction (62M20) Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35) Diffusion processes (60J60) Prediction theory (aspects of stochastic processes) (60G25) Fokker-Planck equations (35Q84)

Related Items (33)

Continuous Time Limit of the Stochastic Ensemble Kalman Inversion: Strong Convergence Analysis ⋮ Log-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models ⋮ Multilevel estimation of normalization constants using ensemble Kalman-Bucy filters ⋮ Perturbations and projections of Kalman-Bucy semigroups ⋮ Autodifferentiable Ensemble Kalman Filters ⋮ A perturbation analysis of stochastic matrix Riccati diffusions ⋮ A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion ⋮ Multilevel Ensemble Kalman–Bucy Filters ⋮ On the mathematical theory of ensemble (linear-Gaussian) Kalman-Bucy filtering ⋮ A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters ⋮ On the Stability and the Uniform Propagation of Chaos of a Class of Extended Ensemble Kalman--Bucy Filters ⋮ Coupled quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles ⋮ Analysis of the ensemble Kalman-Bucy filter for correlated observation noise ⋮ Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler ⋮ Probing robustness of nonlinear filter stability numerically using sinkhorn divergence ⋮ On the Stability of Kalman--Bucy Diffusion Processes ⋮ Two-timescale stochastic gradient descent in continuous time with applications to joint online parameter estimation and optimal sensor placement ⋮ Diffusion Map-based Algorithm for Gain Function Approximation in the Feedback Particle Filter ⋮ Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations ⋮ Stability Properties of Systems of Linear Stochastic Differential Equations with Random Coefficients ⋮ On Stability of a Class of Filters for Nonlinear Stochastic Systems ⋮ On one-dimensional Riccati diffusions ⋮ A second order analysis of McKean-Vlasov semigroups ⋮ On the stability and the concentration of extended Kalman-Bucy filters ⋮ Multilevel ensemble Kalman filtering for spatio-temporal processes ⋮ On the stability of matrix-valued Riccati diffusions ⋮ On the robustness of Riccati flows to complete model misspecification ⋮ Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models ⋮ Well posedness and convergence analysis of the ensemble Kalman inversion ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ An explicit Floquet-type representation of Riccati aperiodic exponential semigroups ⋮ Derivation of ensemble Kalman–Bucy filters with unbounded nonlinear coefficients ⋮ Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Damped oscillations of linear systems. A mathematical introduction
• On the convergence of the ensemble Kalman filter.
• Catastrophic filter divergence in filtering nonlinear dissipative systems
• An approach to stable indirect adaptive control
• A class of Wasserstein metrics for probability distributions
• An alternative stability analysis framework for adaptive control
• Sufficient conditions for stability of linear time-varying systems
• The Riccati equation
• Dichotomies in stability theory
• Stability properties of Kalman-Bucy filters
• Matrix Riccati equations in control and systems theory
• Logarithmic Sobolev inequalities for some nonlinear PDE's.
• On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs
• Probabilistic approach for granular media equations in the non-uniformly convex case
• Global theory of the Riccati equation
• Nonlinear stability and ergodicity of ensemble based Kalman filters
• A Birkhoff Contraction Formula with Applications to Riccati Equations
• A miscellany of results of an equation of Count J. F. Riccati
• Inequalities for the Trace of Matrix Exponentials
• Dynamic Observers as Asymptotic Limits of Recursive Filters: Special Cases
• The Sensitivity of the Matrix Exponential
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• On the Stability of Kalman--Bucy Diffusion Processes
• Asymptotic Stability of the Optimal Filter with Respect to Its Initial Condition
• Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
• Finite Dimensional Linear Systems
• On the Differential Equations Satisfied by Conditional Probablitity Densities of Markov Processes, with Applications
• Linear theory for filtering nonlinear multiscale systems with model error
• Filtering Complex Turbulent Systems
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
• On the optimal filtering of diffusion processes
• On a Matrix Riccati Equation of Stochastic Control
• On Determining the Structure of A by Analyzing $e^{At} $
• A matrix trace inequality
• A matrix trace inequality

This page was built for publication: On the stability and the uniform propagation of chaos properties of ensemble Kalman-Bucy filters