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The Hybrid Monte Carlo Algorithm on Hilbert Space

Wednesday 30th June 2010 - 11:30 to 12:20
INI Seminar Room 1
Hybrid Monte Carlo methods are a class of algorithms for sampling probability measures defined via a density with respect to Lebesgue measure. However, in many applications the probability measure of interest is on an infinite dimensional Hilbert space and is defined via a density with respect to a Gaussian measure. I will show how the Hybrid Monte Carlo methodology can be extended to this Hilbert space setting. A key building block is the study of measure preservation properties for certain semilinear partial differential equations of Hamiltonian type, and approximation of these equations by volume-preserving integrators. Joint work with A. Beskos (UCL), F. Pinski (Cincinnati) and J.-M. Sanz-Serna (Valladolid).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons