A Continuous-Time Ehrenfest Model with Catastrophes and Its Jump-Diffusion Approximation

We consider a continuous-time Ehrenfest model defined over the integers from $$-N$$-N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe istantaneously 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.

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