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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.Comment: 12 page
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