Dynamical large deviations of countable reaction networks under a weak reversibility condition
- Patterson, Robert I. A.
- Renger, D. R. Michiel
2010 Mathematics Subject Classification
- 60F10 60J25 80A30 82C22
- chemical reaction networks, Markov processes, large deviations
A 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.