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

作者：Dharmaraja Selvamuthu; Di Crescenzo Antonio^*; Giorno Virginia; Nobile Amelia G

来源：Journal of Statistical Physics, 2015, 161(2): 326-345.

DOI：10.1007/s10955-015-1336-4

• Transient probabilities
• Steady-state probabilities
• First passage time
• Ornstein-Uhlenbeck process

We consider a continuous-time Ehrenfest model defined over the integers from 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.

• 出版日期2015-10