Claudio Del Sole
Stochastic models of Chemical Reaction Networks: multiscale approximations and convergence.
Rel. Paola Siri, Enrico Bibbona, Franco Fagnola. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2020
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Abstract
Chemical reaction networks are mathematical models widely used to describe the dynamical behaviour of systems in biology, epidemiology, chemistry. In such models, individual units (e.g. molecules), belonging to different groups (e.g. chemical species), interact with each other according to specific laws, named reactions, which may be represented in a graph. Reactions are usually modelled as stochastic counting processes, so that the number of molecules in the system for each species is described by a continuous time Markov chain. When the number of molecules is very high, species dynamics may be suitably described in terms of chemical concentrations, and the stochastic model is well approximated by a deterministic, continuous dynamical system.
However, in some specific cases, such continuous limit proves to be unsatisfactory, and the intrinsic discreteness of the model cannot be disregarded
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