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Conditions for uniform in time convergence: applications to averaging, numerical discretisations and mean-field systems
Katharina Schuh, Iain Souttar
We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist…
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.…
Convergence of kinetic Langevin samplers for non-convex potentials
Katharina Schuh, Peter A. Whalley
We study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We provide contraction results in -Wasserstein distance for n…
Long-time behavior for discretization schemes of Fokker-Planck equations via couplings
Ansgar Jüngel, Katharina Schuh
Continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations are constructed. Sufficient conditions under which quantitative exponent…