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A complete description of dynamics generated by birth-and-death problem: a semigroup approach

Jacek Banasiak — 2003

Banach Center Publications

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.

Around the Kato generation theorem for semigroups

Jacek Banasiak;  Mirosław Lachowicz — 2007

Studia Mathematica

We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.

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