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- ItemDynamical large deviations of countable reaction networks under a weak reversibility condition(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Patterson, Robert I.A.; Renger, D.R. MichielA dynamic large deviations principle for a countable reaction network including coagulation-fragmentation models is proved. The rate function is represented as the infimal cost of the reaction fluxes and a minimiser for this variational problem is shown to exist. A weak reversibility condition is used to control the boundary behaviour and to guarantee a representation for the optimal fluxes via a Lagrange multiplier that can be used to construct the changes of measure used in standard tilting arguments. Reflecting the pure jump nature of the approximating processes, their paths are treated as elements of a BV function space.
- ItemLarge deviations of reaction fluxes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Patterson, Robert I.A.; Renger, D.R. MichielWe study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction fluxes under general assumptions that include mass-action kinetics. This result immediately implies the dynamic large deviations for the empirical concentration.