We consider a continuous-time Markov chain (CTMC) whose state space is
partitioned into aggregates, and each aggregate is assigned a probability
measure. A sufficient condition for defining a CTMC over the aggregates is
presented as a variant of weak lumpability, which also characterizes that the
measure over the original process can be recovered from that of the aggregated
one. We show how the applicability of de-aggregation depends on the initial
distribution. The application section is a major aspect of the article, where
we illustrate that the stochastic rule-based models for biochemical reaction
networks form an important area for usage of the tools developed in the paper.
For the rule-based models, the construction of the aggregates and computation
of the distribution over the aggregates are algorithmic. The techniques are
exemplified in three case studies.