An infinite particle system with continual input and random death

At times n = 0, 1, 2, · · · a Poisson number of particles enter each state of a countable state space. The particles then move independently according to the transition law of a Markov chain, until their death which occurs at a random time. Several limit theorems are then proved for various functionals of this infinite particle system. In particular, laws of large numbers and central limit theorems are proved.

An infinite particle system with continual input and random death

At times n = 0, 1, 2, · · · a Poisson number of particles enter each state of a countable state space. The particles then move independently according to the transition law of a Markov chain, until their death which occurs at a random time. Several limit theorems are then proved for various functionals of this infinite particle system. In particular, laws of large numbers and central limit theorems are proved.