Birth–death process

Summary

A birth–death process is a continuous-time Markov chain on the integers $0, 1, 2, \ldots$ that moves one step up or one step down at each jump. The state is read as the size of a population: a step up is a birth and a step down is a death. When it has a stationary distribution, that distribution has an explicit product formula. It is the basic model for queues, population growth and chemical reactions.