A complete description of dynamics generated by birth-and-death problem: a semigroup approach
Volume 63 / 2003
Banach Center Publications 63 (2003), 123-163
MSC: Primary 47D06; Secondary 60J80
DOI: 10.4064/bc63-0-5
Abstract
We shall present necessary and sufficient conditions for both conservativity and uniqueness of solutions to birth-and-death system of equations using methods of semigroup theory. The derived conditions correspond to the uniqueness criteria for forward and backward birth-and-death systems due to Reuter, \cite{RL, R57, And}, that were derived in a different context by Markov processes' techniques.
