Upper bounding the average residence times in partially observed steady-state Markov jump processes

Several types of stochastic dynamics can be modeled as a continuous-time Markov jump process among a finite number of sites. Within such framework, we face the problem of getting an upper bound on the average residence time of the system in a given site β (i.e., the average lifetime of the site) if what we can observe is only the permanence of the system in an adjacent site α and the occurrence of the transitions α→β. Supposing to have a long time record of this partial monitoring of the network under steady-state conditions, we show that an upper bound on the average time spent in the unobserved site can indeed be given. The bound is formally proved, tested by means of simulations, and illustrated for a multicyclic enzymatic reaction scheme.