**Papers Published**

- with Mattingly, JC; Pillai, NS; Stuart, AM,
*Diffusion limits of the random walk Metropolis algorithm in high dimensions*, Annals of Applied Probability, vol. 22 no. 3 (June, 2011), pp. 881-930, Institute of Mathematical Statistics

(last updated on 2019/05/22)**Abstract:**

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.