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math.PR2025

Piecewise deterministic sampling with splitting schemes

Andrea Bertazzi, Paul Dobson, Pierre Monmarché

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schem…

math.PR2025

Free energy Wasserstein gradient flow and their particle counterparts: toy model, (degenerate) PL inequalities and exit times

Pierre Monmarché

In finite dimension, the long-time and metastable behavior of a gradient flow perturbated by a small Brownian noise is well understood. A similar situation arises when a Wasserstei…

math.PR2025

Exponential Ergodicity in Relative Entropy and -Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs

Xing Huang, Eva Kopfer, Pierre Monmarché +1

In this paper, we derive exponential ergodicity in relative entropy for general kinetic SDEs under a partially dissipative condition. It covers non-equilibrium situations where the…

math.PR2025

Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent

Pierre Germain, Pierre Monmarché

For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of differe…

math.PR2024

Non-asymptotic entropic bounds for non-linear kinetic Langevin sampler with second-order splitting scheme

Pierre Monmarché, Katharina Schuh

The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed.…