Diffusion Limits of MCMC Methods
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Mon, 15/06/2009 14:15 |
Professor Andrew Stuart (University of Warwick) |
Stochastic Analysis Seminar  |
Oxford-Man Institute |
| 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) | |||