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dr inż. Małgorzata Pułka
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- Assistant professor at Institute of Applied Mathematics
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total: 8
Catalog Publications
Year 2019
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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
Year 2018
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublicationThis paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
Year 2015
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
Year 2014
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Mieszanie w klasie niejednorodnych łańcuchów Markowa i kwadratowych operatorów stochastycznych
PublicationRozprawa doktorska poświęcona jest zagadnieniu asymptotycznych własności w klasie nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym oraz w klasie kwadratowych operatorów stochastycznych. W pierwszej kolejności definiowane są różne rodzaje asymptotycznego zachowania (mieszania) niejednorodnych łańcuchów Markowa odpowiadające zbieżności w normowej i mocnej topologii operatorowej oraz omówione są relacje...
Year 2013
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently. In the present work we discuss biological interpretations that can be attributed to them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
Year 2012
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
Year 2011
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On the mixing property and the ergodic principle for nonhomogeneous Markov chains
PublicationW pracy rozważane są różne typy zachowania granicznego nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym. Badana jest struktura geometryczna zbioru łańcuchów Markowa w normowej i mocnej topologii operatorowej.
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