Continuous Dependence in a Problem of Convergence of Random Iteration

被引：1

作者：

Kapica, Rafal ^{[1
]}

Komorek, Dawid ^{[1
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, al A Mickiewicza 30, PL-30059 Krakow, Poland

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2023年 / 22卷 / 02期

关键词：

Random iteration; Markov operator; Invariant measure; Hutchinson distance; Fortet-Mourier distance; Continuous dependence on the given function; Perpetuities; FRACTALS;

D O I：

10.1007/s12346-023-00763-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that an invariant measure of a Markov operator that is contracting in the Hutchison distance, acting on a space of Borel probability measures on a Polish space, depends continuously on the given operator. In addition, we establish an estimate for a distance between invariant measures. Some applications to the weak limit of iterates of random-valued functions (in particular, the so-called random affine maps, occuring, e.g., in perpetuities analysis) are also given.

引用

页数：19

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