Guided simulation of conditioned chemical reaction networks

Let X be a chemical reaction process, modeled as a multi-dimensional continuous-time jump process. Assume that at given times 0<t1<⋯<tn, linear combinations vi=LiX(ti),i=1,⋯,n are observed for given matrices Li. We show how the process that is conditioned on hitting the states v1,⋯,vn is obtained by a change of measure on the law of the unconditioned process. This results in an algorithm for obtaining weighted samples from the conditioned process. Our results are illustrated by numerical simulations.