181 citations · 446 across the 49 of their papers we have counts for
27 papers · 1 filter
Fluctuations and Long-Time Stability of Multivariate Ensemble Kalman Filters
Pierre Del Moral, Bouchra Nasri, Bruno Rémillard
We develop a self contained stochastic perturbation theory for discrete generation and multivariate Ensemble Kalman filters. Unlike their continuous-time counterparts, discrete EnK…
On the Particle Approximation of Lagged Feynman-Kac Formulae
Elsiddig Awadelkarim, Michel Caffarel, Pierre Del Moral +1
In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and…
On Time Uniform Wong-Zakai Approximation Theorems
Pierre Del Moral, Shulan Hu, Ajay Jasra +2
We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in man…
On the Stability of Positive Semigroups
Pierre del Moral, Emma Horton, Ajay Jasra
The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction metho…
Quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles
Pierre del Moral, Emma Horton
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-defini…
Backward Nonlinear Smoothing Diffusions
Brian D. O. Anderson, Adrian N. Bishop, Pierre Del Moral +1
We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribu…
Backward It{ô}-Ventzell and stochastic interpolation formulae
Pierre del Moral, Sumeetpal Sidhu Singh
We present a novel backward It{ô}-Ventzell formula and an extension of the Aleeksev-Gröbner interpolating formula to stochastic flows. We also present some natural spectral conditi…
A variational approach to nonlinear and interacting diffusions
Marc Arnaudon, Pierre Del Moral
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential method…
On One-Dimensional Riccati Diffusions
Adrian N. Bishop, Pierre Del Moral, Kengo Kamatani +1
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential…
An Introduction to Wishart Matrix Moments
Adrian N. Bishop, Pierre Del Moral, Angele Niclas
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects…
A perturbation analysis of stochastic matrix Riccati diffusions
Adrian N. Bishop, Pierre Del Moral, Angele Niclas
Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic…
Perturbations and projections of Kalman-Bucy semigroups
Adrian N. Bishop, Pierre Del Moral, Sahani D. Pathiraja
We analyse various perturbations and projections of Kalman-Bucy semigroups and Riccati equations. For example, covariance inflation-type perturbations and localisation methods (pro…
On the stability and the uniform propagation of chaos of a class of Extended Ensemble Kalman-Bucy filters
Pierre Del Moral, Aline Kurtzmann, Julian Tugaut
This article is concerned with the exponential stability and the uniform propagation of chaos properties of a class of Extended Ensemble Kalman-Bucy filters with respect to the tim…
On the Stability and the Exponential Concentration of Extended Kalman-Bucy filters
Pierre Del Moral, Aline Kurtzmann, Julian Tugaut
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially obser…
On the stability and the uniform propagation of chaos properties of Ensemble Kalman-Bucy filters
Pierre Del Moral, Julian Tugaut
The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. Thi…
Exponential mixing properties for time inhomogeneous diffusion processes with killing
Pierre Del Moral, Denis Villemonais
We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of with a smooth boundary. The process…
On particle Gibbs Markov chain Monte Carlo models
P. Del Moral, R. Kohn, F. Patras
This article analyses a new class of advanced particle Markov chain Monte Carlo algorithms recently introduced by Andrieu, Doucet, and Holenstein (2010). We present a natural inter…
A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants
Jean Bérard, Pierre Del-Moral, Arnaud Doucet
This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-k…
On parallel implementation of Sequential Monte Carlo methods: the island particle model
Christelle Vergé, Cyrille Dubarry, Pierre Del Moral +1
The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we st…
Feynman-Kac particle integration with geometric interacting jumps
Pierre Del Moral, Pierre E. Jacob, Anthony Lee +2
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general ty…
Nonasymptotic analysis of adaptive and annealed Feynman-Kac particle models
François Giraud, Pierre Del Moral
Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac mode…
Moderate Deviations for Mean Field Particle Models
Pierre Del Moral, Shulan Hu, Liming Wu
This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occup…
Fluctuations of Interacting Markov Chain Monte Carlo Methods
Bernard Bercu, Pierre Del Moral, Arnaud Doucet
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algor…
Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations
Pierre Del Moral, Arnaud Doucet
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong…