Markov population processes

Abstract

Summary: The processes of the title have frequently been used to represent situations involving numbers of individuals in different categories or colonies. In such processes the state at any time is represented by the vector n = (n₁, n₂, …, n_k), where n_t is the number of individuals in the ith colony, and the random evolution of n is supposed to be that of a continuous-time Markov chain. The jumps of the chain may be of three types, corresponding to the arrival of a new individual, the departure of an existing one, or the transfer of an individual from one colony to another.