A Stochastic Hybrid Approximation for Chemical Kinetics Based on the Linear Noise Approximation

The Linear Noise Approximation (LNA) is a continuous approximation of the CME, which improves scalability and is accurate for those reactions satisfying the leap conditions. We formulate a novel stochastic hybrid approximation method for chemical reaction networks based on adaptive partitioning of the species and reactions according to leap conditions into two classes, one solved numerically via the CME and the other using the LNA. The leap criteria are more general than partitioning based on population thresholds, and the method can be combined with any numerical solution of the CME. We then use the hybrid model to derive a fast approximate model checking algorithm for Stochastic Evolution Logic (SEL). Experimental evaluation on several case studies demonstrates that the techniques are able to provide an accurate stochastic characterisation for a large class of systems, especially those presenting dynamical stiffness, resulting in significant improvement of computation time while still maintaining scalability.