  We consider the stochastic gene expression process with inter-state
flip-flops. An exact steady-state solution to the master equation is
calculated. One of the main goals in this paper is to investigate whether the
probability distribution of gene copies contains even-odd number oscillations.
A master equation previously derived in the adiabatic limit of fast switching
by Kepler and Elston \cite{kepler} suggests that the oscillations should be
present. However our analysis demonstrates that the oscillations do not happen
not only in the adiabatic case but they are entirely absent. We discuss the
adiabatic approximation in detail. The other goal is to establish the master
equation that takes into account external fluctuations that is similar to the
master equation in the adiabatic approximation. The equation allows even-odd
oscillations. The reason the behaviour occurs is an underlying interference of
Poisson and Gaussian processes. The master equation contains an extra term that
describes the gene copy number unconventional diffusion and is responsible for
the oscillations. We also point out to a similar phenomenon in quantum physics.
