Exact targeting of Gibbs distributions using velocity-jump processes - Université de Rennes Accéder directement au contenu
Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2022

Exact targeting of Gibbs distributions using velocity-jump processes

Résumé

This work introduces and studies a new family of velocity jump Markov processes directly amenable to exact simulation with the following two properties: i) trajectories converge in law when a time-step parameter vanishes towards a given Langevin or Hamil-tonian dynamics; ii) the stationary distribution of the process is always exactly given by the product of a Gaussian (for velocities) by any target log-density whose gradient is pointwise computabe together with some additional explicit appropriate upper bound. The process does not exhibit any velocity reflections (jump sizes can be controlled) and is suitable for the 'factorization method'. We provide a rigorous mathematical proof of: i) the small time-step convergence towards Hamiltonian/Langevin dynamics, as well as ii) the exponentially fast convergence towards the target distribution when suitable noise on velocity is present. Numerical implementation is detailed and illustrated.
Fichier principal
Vignette du fichier
main.pdf (975.42 Ko) Télécharger le fichier
HAL/main.toc (2.73 Ko) Télécharger le fichier
HAL/simu (4.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02916073 , version 1 (20-08-2020)
hal-02916073 , version 2 (13-09-2020)

Identifiants

Citer

Pierre Monmarché, Mathias Rousset, Pierre-André Zitt. Exact targeting of Gibbs distributions using velocity-jump processes. Stochastics and Partial Differential Equations: Analysis and Computations, 2022, ⟨10.1007/s40072-022-00247-9⟩. ⟨hal-02916073v2⟩
222 Consultations
87 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More