4 papers · 2 filters
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…
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…
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…
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…