ANZIAM  J.  48 (2007), 409-418

A note on three stochastic processes with immigration

J. Gani   Mathematical Sciences Institute   Australian National University   Canberra ACT 0200   Australia   gani@maths.anu.edu.au and L. Stals   Mathematical Sciences Institute   Australian National University   Canberra ACT 0200   Australia   stals@maths.anu.edu.au

Abstract

Three stochastic processes, the birth, death and birth-death processes, subject to immigration can be decomposed into the sum of each process in the absence of immigration and an independent process. We examine these independent processes through their probability generating functions (pgfs) and derive their expectations.

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