  We consider a continuous-time Ehrenfest model defined over the integers from
-N to N, and subject to catastrophes occurring at constant rate. The effect of
each catastrophe instantaneously resets the process to state 0. We investigate
both the transient and steady-state probabilities of the above model. Further,
the first passage time through state 0 is discussed. We perform a
jump-diffusion approximation of the above model, which leads to the
Ornstein-Uhlenbeck process with catastrophes. The underlying jump-diffusion
process is finally studied, with special attention to the symmetric case
arising when the Ehrenfest model has equal upward and downward transition
rates.
