Abstract
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.