Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-7188 Masterarbeit / Diplomarbeit Helfmann, Luzie Stochastic Modeling of Interacting Agent Systems 2018 68 urn:nbn:de:0297-zib-71887 Numerical Mathematics OPUS4-7339 Wissenschaftlicher Artikel Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof From interacting agents to density-based modeling with stochastic PDEs Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. 2021 31 Communications in Applied Mathematics and Computational Science 16 1 1 32 10.2140/camcos.2021.16.1 Numerical Mathematics OPUS4-7345 misc Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof From interacting agents to density-based modeling with stochastic PDEs Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. 2019 urn:nbn:de:0297-zib-73456 Numerical Mathematics