Affiliations: [a] Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, Netherlands. E-mail: [email protected] | [b] Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland. E-mail: [email protected] | [c] Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland. E-mail: [email protected] | [d] Institute of Mathematics, Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland | [e] National Quantum Information Center of Gdańsk, ul. Wł. Andersa 27, 81-824 Sopot, Poland. E-mail: [email protected]
Correspondence:
[*]
Corresponding address: Tomasz Szarek, Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland. E-mail: [email protected].
Abstract: The law of the iterated logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell cycle model examined by Lasota and Mackey [J. Math. Biol. 38 (1999), 241–261].
Keywords: law of the iterated logarithm, Markov operators
