Random Iteration with Place Dependent Probabilities

• Autorzy: Kapica Rafał , Ślęczka Maciej

Identyfikatory

DOI

10.37190/0208-4147.40.1.8

• Języki publikacji: EN

Abstrakty

EN

We consider Markov chains arising from random iteration of functions S_θ : X → X, θ ϵ Θ, where X is a Polish space and Θ is an arbitrary set of indices. At x ϵ X, θ is sampled from a distribution ϑ_x on Θ, and the ϑ_x are different for different x. Exponential convergence to a unique invariant measure is proved. This result is applied to the case of random affine transformations on R^d, giving the existence of exponentially attractive perpetuities with place dependent probabilities.

Słowa kluczowe

EN

random iteration of functions; exponential convergence; invariant measure; perpetuities

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 1
• Strony: 119--137
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Kapica Rafał

• Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland

autor

Ślęczka Maciej

• Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007 Katowice, Poland

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).