--- _id: '3838' abstract: - lang: eng text: We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe net- works of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient prob- ability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We im- plemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology. author: - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Maria full_name: Mateescu, Maria last_name: Mateescu - first_name: Linar full_name: Mikeev, Linar last_name: Mikeev - first_name: Verena full_name: Wolf, Verena last_name: Wolf citation: ama: 'Henzinger TA, Mateescu M, Mikeev L, Wolf V. Hybrid numerical solution of the chemical master equation. In: Springer; 2010:55-65. doi:10.1145/1839764.1839772' apa: 'Henzinger, T. A., Mateescu, M., Mikeev, L., & Wolf, V. (2010). Hybrid numerical solution of the chemical master equation (pp. 55–65). Presented at the CMSB: Computational Methods in Systems Biology, Trento, Italy: Springer. https://doi.org/10.1145/1839764.1839772' chicago: Henzinger, Thomas A, Maria Mateescu, Linar Mikeev, and Verena Wolf. “Hybrid Numerical Solution of the Chemical Master Equation,” 55–65. Springer, 2010. https://doi.org/10.1145/1839764.1839772. ieee: 'T. A. Henzinger, M. Mateescu, L. Mikeev, and V. Wolf, “Hybrid numerical solution of the chemical master equation,” presented at the CMSB: Computational Methods in Systems Biology, Trento, Italy, 2010, pp. 55–65.' ista: 'Henzinger TA, Mateescu M, Mikeev L, Wolf V. 2010. Hybrid numerical solution of the chemical master equation. CMSB: Computational Methods in Systems Biology, 55–65.' mla: Henzinger, Thomas A., et al. Hybrid Numerical Solution of the Chemical Master Equation. Springer, 2010, pp. 55–65, doi:10.1145/1839764.1839772. short: T.A. Henzinger, M. Mateescu, L. Mikeev, V. Wolf, in:, Springer, 2010, pp. 55–65. conference: end_date: 2010-10-01 location: Trento, Italy name: 'CMSB: Computational Methods in Systems Biology' start_date: 2010-09-29 date_created: 2018-12-11T12:05:27Z date_published: 2010-09-29T00:00:00Z date_updated: 2021-01-12T07:52:33Z day: '29' ddc: - '004' department: - _id: ToHe doi: 10.1145/1839764.1839772 file: - access_level: open_access checksum: 81cb6f0babd97151b171d1ce86582831 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:55Z date_updated: 2020-07-14T12:46:16Z file_id: '5179' file_name: IST-2012-68-v1+1_Hybrid_Numerical_Solution_of_the_Chemical_Master_Equation.pdf file_size: 671790 relation: main_file file_date_updated: 2020-07-14T12:46:16Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Submitted Version page: 55 - 65 publication_status: published publisher: Springer publist_id: '2356' pubrep_id: '68' quality_controlled: '1' scopus_import: 1 status: public title: Hybrid numerical solution of the chemical master equation type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2010' ...