Before revision:  In this paper we aim to show that the concept of ensemble of trajectories can be applied to a variety of stochastic models of gene expression and hence , apart from asymptotic behavior of remote tails of probability distributions of the dynamical observables, generating functions for the cumulants of these observables can easily be obtained.
After revision:  In this paper we aim to show that the concept of ensemble of trajectories can be applied to a variety of stochastic models of gene expression and hence , apart from asymptotic behavior of remote tails of probability distributions of the dynamical observables, generating functions for the cumulants of this observable can also be obtained.