Langevin diffusions and the Metropolis-adjusted Langevin algorithm

Xifara, Tatiana and Sherlock, Christopher and Livingstone, Samuel and Byrne, Simon and Girolami, Mark (2014) Langevin diffusions and the Metropolis-adjusted Langevin algorithm. Statistics and Probability Letters, 91. pp. 14-19. ISSN 0167-7152

Abstract

We describe a Langevin diffusion with a target stationary density with respect to Lebesgue measure, as opposed to the volume measure of a previously-proposed diffusion. The two are sometimes equivalent but distinct in general and lead to different Metropolis-adjusted Langevin algorithms, which we compare.