@article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Geometric Approach to Constrained Molecular Dynamics and Free Energy}, series = {Comm. Math. Sci.}, volume = {3}, journal = {Comm. Math. Sci.}, number = {1}, pages = {1 -- 20}, year = {2005}, language = {en} } @article{SchuetteNoeMeerbachetal.2009, author = {Sch{\"u}tte, Christof and No{\´e}, Frank and Meerbach, E. and Metzner, Ph. and Hartmann, Carsten}, title = {Conformation Dynamics}, series = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, journal = {Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.),}, publisher = {EMS publishing house}, doi = {10.4171/056-1/15}, pages = {297 -- 335}, year = {2009}, language = {en} } @article{SchuetteWalterHartmannetal.2004, author = {Sch{\"u}tte, Christof and Walter, J. and Hartmann, Carsten and Huisinga, Wilhelm}, title = {An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations}, series = {Multiscale Model. Simul.}, volume = {2}, journal = {Multiscale Model. Simul.}, number = {3}, doi = {10.1137/030600308}, pages = {501 -- 526}, year = {2004}, language = {en} } @article{SchuetteWinkelmannHartmann2012, author = {Sch{\"u}tte, Christof and Winkelmann, Stefanie and Hartmann, Carsten}, title = {Optimal control of molecular dynamics using Markov state models}, series = {Math. Program. (Series B)}, volume = {134}, journal = {Math. Program. (Series B)}, number = {1}, doi = {10.1007/s10107-012-0547-6}, pages = {259 -- 282}, year = {2012}, language = {en} } @article{HartmannSchuette2008, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Balancing of partially-observed stochastic differential equations}, series = {47th IEEE Conference on Decision and Control}, journal = {47th IEEE Conference on Decision and Control}, doi = {10.1109/CDC.2008.4739161}, pages = {4867 -- 4872}, year = {2008}, language = {en} } @article{LatorreHartmannSchuette2010, author = {Latorre, J. and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Free energy computation by controlled Langevin processes}, series = {Procedia Computer Science}, volume = {1}, journal = {Procedia Computer Science}, number = {1}, doi = {10.1016/j.procs.2010.04.179}, pages = {1591 -- 1600}, year = {2010}, language = {en} } @article{SchaeferBungHartmannSchmidtetal.2011, author = {Sch{\"a}fer-Bung, B. and Hartmann, Carsten and Schmidt, Burkhard and Sch{\"u}tte, Christof}, title = {Dimension reduction by balanced truncation}, series = {J. Chem. Phys.}, volume = {135}, journal = {J. Chem. Phys.}, number = {1}, pages = {014112}, year = {2011}, language = {en} } @article{HartmannSchuette2007, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Comment on Two Distinct Notions of Free Energy}, series = {Physica D}, volume = {228}, journal = {Physica D}, number = {1}, doi = {10.1016/j.physd.2007.02.006}, pages = {59 -- 63}, year = {2007}, language = {en} } @article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Constrained Hybrid Monte-Carlo Algorithm and the Problem of Calculating the Free Energy in Several Variables}, series = {Z. Angew. Math. Mech.}, volume = {85}, journal = {Z. Angew. Math. Mech.}, number = {10}, doi = {10.1002/zamm.200410218}, pages = {700 -- 710}, year = {2005}, language = {en} } @article{HartmannSchuetteWeberetal., author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Weber, Marcus and Zhang, Wei}, title = {Importance sampling in path space for diffusion processes with slow-fast variables}, series = {Probability Theory and Related Fields}, journal = {Probability Theory and Related Fields}, doi = {10.1007/s00440-017-0755-3}, pages = {1 -- 52}, abstract = {Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.}, language = {en} }