Let X be a chemical reaction process, modeled as a multi-dimensional continuous-time jump process. Assume that at given times \(0< t_1< \cdots <t_n\) , linear combinations \(v_i = L_i X(t_i),\, i=1,\dots ,n\) are observed for given matrices \(L_i\) . We show how the process that is conditioned on hitting the states \(v_1,\dots , v_n\) 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.
