# Exponential convergence of Langevin distributions and their discrete approximations

@article{Roberts1996ExponentialCO, title={Exponential convergence of Langevin distributions and their discrete approximations}, author={Gareth O. Roberts and Richard L. Tweedie}, journal={Bernoulli}, year={1996}, volume={2}, pages={341-363} }

In this paper we consider a continuous-time method of approximating a given distribution using the Langevin diusion dLtdWt 1 2 r log (Lt)dt. We ®nd conditions under this diusion converges exponentially quickly to or does not: in one dimension, these are essentially that for distributions with exponential tails of the form (x)/ exp (y |x| , 0< <1, exponential convergence occurs if and only if 1. We then consider conditions under which the discrete approximations to the diusion converge. We…

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