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We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our work is a new density formula for random variables in the…
We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but…
We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…
We consider classical solutions to the kinetic Fokker-Planck equation on a bounded domain $\mathcal O \subset~\mathbb{R}^d$ in position, and we obtain a probabilistic representation of the solutions using the Langevin diffusion process with…
We consider various one-dimensional non-equilibrium models, namely the {\it diffusion-limited pair-annihilation and creation model} (DPAC) and its unbiased version (the Lushnikov's model), the DPAC model with particle injection (DPACI), as…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…
Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
Inspired by Kalikow-type decompositions, we introduce a new stochastic model of infinite neuronal networks, for which we establish sharp oracle inequalities for Lasso methods and restricted eigenvalue properties for the associated Gram…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…
Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with non-zero drift. Let the process be stationary with product Bernoulli invariant distribution at density \rho. Place a second class particle…
We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…