ABSTRACT
This chapter introduces a flexible but rather powerful variation on the population processes that we have studied that can be used to generate a wide variety of models and the fluctuation phenomena that are associated with them. The immigrant pair model has deaths that occur by the usual mechanism and immigrants that arrive in couples. It is a straightforward generalisation to envisage a situation where the immigrants arrive in r-tuplets at rates νr that are particular to the order r. Provided that these rates are all positive quantities, they can be chosen arbitrarily. Indeed, the rates can be chosen so that the steady state distribution has a prescribed form. Consequently, once the techniques for deriving, solving and analysing the basic Markov population process have been mastered, the death-multiple immigration model can be used to generate the probability distributions and evolution characteristics of more complex systems that will be discussed in later chapters.
