Krzysztof Bartoszek: Asymptotic properties of quadratic stochastic operators acting on the L1 space

Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the l1 space (Bartoszek and Pulka 2013). It turns out that in principle most of the results can be carried over to the \(L1\) space. However due to topological properties, weak convergence does not imply strong, of this space one has to restrict in some situations to kernel quadratic stochastic operators. We will discuss the uniform and strong asymptotic stability of quadratic stochastic operators in terms of convergence of an associated nonhomogeneous Markov chains.