Methodology And Computing In Applied Probability

, Volume 4, Issue 4, pp 337-357

First online:

Langevin Diffusions and Metropolis-Hastings Algorithms

  • G. O. RobertsAffiliated withDepartment of Mathematics and Statistics, Lancaster University
  • , O. StramerAffiliated withDepartment of Statistics and Actuarial Science, University of Iowa

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We consider a class of Langevin diffusions with state-dependent volatility. The volatility of the diffusion is chosen so as to make the stationary distribution of the diffusion with respect to its natural clock, a heated version of the stationary density of interest. The motivation behind this construction is the desire to construct uniformly ergodic diffusions with required stationary densities. Discrete time algorithms constructed by Hastings accept reject mechanisms are constructed from discretisations of the algorithms, and the properties of these algorithms are investigated.

MCMC Langevin diffusions and algorithms