Lie algebraic discussions for time-inhomogeneous linear birth-death   processes with immigration
  Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without 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 is understood from the viewpoint of the finiteness of the dimensionality of the Lie algebra. 
Jun Ohkubo
math-ph cond-mat.stat-mech math.MP