As many quantities of cell biological interest are present in discrete copy number within the cell (single DNAs, dozens of mRNAs, hundreds of proteins), tools from discrete stochastic mathematics are often used to analyse and model cellular noise. In particular, master equation treatments – where the probabilities  of observing a system in a state  at time  are linked through ODEs – have proved particularly fruitful. A canonical model for noise gene expression, where the processes of DNA activation, transcription and translation are all represented as Poisson processes with given rates, gives a master equation which may be solved exactly (with generating functions) under various assumptions or approximated with stochastic tools like Van Kampen's system size expansion.
Numerically, the Gillespie algorithm or stochastic simulation algorithm is often used to create realisations of stochastic cellular processes, from which statistics can be calculated.
The problem of inferring the values of parameters in stochastic models (parametric inference) for biological processes, which are typically characterised by sparse and noisy experimental data, is an active field of research, with methods including Bayesian MCMC and approximate Bayesian computation proving adaptable and robust. Regarding the two-state model, a moment-based method was described for parameters inference from mRNAs distributions.