14:15
Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying efficiency.
In particular they facilitate 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 only been proved for target measures with a product structure, severely limiting their applicability to real applications. The purpose of this talk is to desribe a research program aimed at identifying diffusion limits for a class of naturally occuring problems, found by finite dimensional approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure.
The diffusion limit to a Hilbert space valued SDE (or SPDE) is proved.
Joint work with Natesh Pillai (Warwick) and Jonathan Mattingly (Duke)