Convergence of preconditioned Hamiltonian Monte Carlo on Hilbert spaces.

In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from Bou-Rabee, Eberle and Zimmer (2020). [ABSTRACT FROM AUTHOR]