  When electric current flows through a molecular junction, the molecule
constantly charges and discharges by tunnelling electrons. These charging and
discharging events occur at specific but random times and separated by
stochastic time intervals. These time intervals can be associated with dwelling
time for a charge (electron or hole) to reside on the molecule. In this paper,
the statistical properties of these time intervals are studied and general
formula for their distribution is derived. The theory is based on the Markovian
master equation which takes into account transitions between vibrational states
of charged and neutral molecule in the junction. Two quantum jump operators are
identified from the Liouvillian of the master equation - one corresponds to
charging of the molecule and the other discharges the molecule back to neutral
state. The quantum jump operators define the conditional probability that given
that the molecule was charged by a tunneling electron at time $t$, the molecule
becomes neutral at later time $t+\tau$ discharging the electron to the drain
electrode. Statistical properties of these time intervals $\tau$ are studied
with the use of this distribution.
