# On Lq Convergence of the Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2101.08688 · HTML: https://mlsanity.com/paper/2101.08688/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 5 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 1 of 1)

- [On the Geometric Ergodicity of Hamiltonian Monte Carlo](https://mlsanity.com/paper/1601.08057/) (2016)

## Built on by (most cited first, 1 of 1)

- [On Convergence of the Alternating Directions SGHMC Algorithm](https://mlsanity.com/paper/2405.13140/) (2024)

## Abstract (arXiv)

We establish Lq convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2≤ q<∞ and weakly for 1<q<2) to the desired target distribution.