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, [10,11,1], that were derived in a different context by Markov processes' techniques.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-5,
author = {Jacek Banasiak},
title = {A complete description of dynamics generated by birth-and-death problem: a semigroup approach},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {123-163},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-5}
}
Jacek Banasiak. A complete description of dynamics generated by birth-and-death problem: a semigroup approach. Banach Center Publications, Tome 60 (2003) pp. 123-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc63-0-5/