A continuous-time Ehrenfest model with catastrophes and its jump-diffusion approximation

Abstract

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.

21 pages, 10 figures

References in corpus (6)

• Diffusion with Stochastic Resetting
• Diffusion with Optimal Resetting
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic resetting
• A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation
• Ehrenfest Model with Large Jumps in Finance

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