@misc{WeberKubeRiemeretal., author = {Weber, Marcus and Kube, Susanna and Riemer, Alexander and Bujotzek, Alexander}, title = {Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9467}, number = {07-03}, abstract = {In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.}, language = {en} } @misc{WeberWalterKubeetal., author = {Weber, Marcus and Walter, Lionel and Kube, Susanna and Deuflhard, Peter}, title = {Stable computation of probability densities for metastable dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9331}, number = {06-39}, abstract = {Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.}, language = {en} }