181 citations · 446 across the 49 of their papers we have counts for
56 papers
A perturbation theory for Feynman-Kac models and their particle interpretations
Pierre Del Moral, Mathieu Gerber
We develop a perturbation analysis of Feynman--Kac models, describing how local errors introduced at each step of the Feynman--Kac recursion propagate over time. Under general cond…
On Bridging Mixture Distributions
Pierre Del Moral, Ajay Jasra, Ke Zhao
The construction and the stability of bridges between mixture probability measures are investigated. Given a collection of Markov transitions bridging the components of two mixture…
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 the Mathematical foundations of Diffusion Monte Carlo
Michel Caffarel, Pierre del Moral, Luc de Montella
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology…
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…
Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods
Pierre Del Moral, Shulan Hu, Ajay Jasra +2
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamic…
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…
Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models
Dan Crisan, Pierre Del Moral, Ajay Jasra +1
In this article we consider the estimation of the log-normalization constant associated to a class of continuous-time filtering models. In particular, we consider ensemble Kalman-B…
On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering
Adrian N. Bishop, Pierre Del Moral
The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models…
Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation
Benjamin Nguyen-Van-Yen, Pierre Del Moral, Bernard Cazelles
We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov j…
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…
An explicit Floquet-type representation of Riccati aperiodic exponential semigroups
Adrian N. Bishop, Pierre Del Moral
The article presents a rather surprising Floquet-type representation of time-varying transition matrices associated with a class of nonlinear matrix differential Riccati equations.…
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…
A Taylor expansion of the square root matrix functional
Pierre Del Moral, Angele Niclas
This short note provides an explicit description of the Fréchet derivatives of the principal square root matrix functional at any order. We present an original formulation that all…
Unbiased Multi-index Monte Carlo
Dan Crisan, Pierre Del Moral, Jeremie Houssineau +1
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from…
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…
A Note on Random Walks with Absorbing barriers and Sequential Monte Carlo Methods
Pierre Del Moral, Ajay Jasra
In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, w…
On the Stability of Kalman-Bucy Diffusion Processes
Adrian N. Bishop, Pierre Del Moral
The Kalman-Bucy filter is the optimal state estimator for an Ornstein-Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Un…