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Strong and weak stability of some Markov operators. (English) Zbl 0992.47016

The paper is devoted to the integral Markov operator \(P\) arising in biomathematics and acting on the space of probabilistic Borel measures. Given such measures \(\mu\) and \(\nu\), sufficient conditions for weak and strong convergence of the sequence \((P^n\mu -P^n\nu)\) to \(0\) are obtained.

MSC:

47B38 Linear operators on function spaces (general)
47B65 Positive linear operators and order-bounded operators
60J05 Discrete-time Markov processes on general state spaces
92D25 Population dynamics (general)
47G10 Integral operators
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