--- res: bibo_abstract: - We present an on-the-fly abstraction technique for infinite-state continuous -time Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic modeling of biological systems. We approximate the transient probability distributions at various time instances by solving a sequence of dynamically constructed abstract models, each depending on the previous one. Each abstract model is a finite Markov chain that represents the behavior of the original, infinite chain during a specific time interval. Our approach provides complete information about probability distributions, not just about individual parameters like the mean. The error of each abstraction can be computed, and the precision of the abstraction refined when desired. We implemented the algorithm and demonstrate its usefulness and efficiency on several case studies from systems biology.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Thomas A foaf_name: Thomas Henzinger foaf_surname: Henzinger foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87 orcid: 0000−0002−2985−7724 - foaf_Person: foaf_givenName: Maria foaf_name: Maria Mateescu foaf_surname: Mateescu foaf_workInfoHomepage: http://www.librecat.org/personId=3B43276C-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Verena foaf_name: Wolf, Verena foaf_surname: Wolf bibo_doi: 10.1007/978-3-642-02658-4_27 bibo_volume: 5643 dct_date: 2009^xs_gYear dct_publisher: Springer@ dct_title: Sliding-window abstraction for infinite Markov chains@ ...