We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon–Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon–Wu equation is given.
Keywords:
present necessary sufficient condition asymptotic stability markov operators acting space signed measures proof based special properties total variation norm method allows consider tjon equation linear form precisely proof asymptotic stability stationary solution tjon equation given
Affiliations des auteurs :
Roksana Brodnicka
1
;
Henryk Gacki
1
1
Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Roksana Brodnicka; Henryk Gacki. Asymptotic stability of a linear Boltzmann-type equation. Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 323-334. doi: 10.4064/am41-4-3
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title = {Asymptotic stability of a linear {Boltzmann-type} equation},
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