Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration

摘要

Analytical solutions for time-inhomogeneous linear birth-death processes withimmigration are derived. While time-inhomogeneous linear birth-death processeswithout immigration have been studied by using a generating function approach,the processes with immigration are here analyzed by Lie algebraic discussions.As a result, a restriction for time-inhomogeneity of the birth-death process isunderstood from the viewpoint of the finiteness of the dimensionality of theLie algebra.