Convergence in Law of Iterates of Weakly Contractive in Mean Random-Valued Functions

被引：0

作者：

Baron, Karol ^{[1
]}

Kapica, Rafal ^{[2
]}

Morawiec, Janusz ^{[1
]}

机构：

[1] Univ Silesia, Inst Math, Bankowa 14, PL-40007 Katowice, Poland

[2] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

来源：

RESULTS IN MATHEMATICS | 2024年 / 79卷 / 02期

关键词：

Iterates of random-valued functions; speed of convergence; FRACTALS;

D O I：

10.1007/s00025-023-02093-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the asymptotic behaviour of the sequence of forward type iterations of a given random-valued vector function on the state space being a separable and complete metric space. Assuming non-linear contraction in mean we prove that the considered sequence converges weakly to a random variable with a finite first moment and independent of the initial state. Moreover, we show that the speed of this convergence does not have to be geometric. We also present examples illustrating the result obtained.

引用

页数：12

共 49 条

[41] A new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of Banach space valued random elements
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[42] Mean convergence theorems for the maximum of normed double sums of Banach space valued random elements under compact uniform integrability conditions
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[43] CONVERGENCE-RATES IN THE MARCINKIEWICZ STRONG LAW OF LARGE NUMBERS FOR BANACH-SPACE VALUED RANDOM-VARIABLES WITH MULTIDIMENSIONAL INDEXES
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[44] Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
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[45] Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
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[46] On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense
Cabrera, Manuel Ordonez
Rosalsky, Andrew
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Volodin, Andrei
TEST, 2021, 30 (01) : 83 - 102
[47] On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense
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Andrew Rosalsky
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TEST, 2021, 30 : 83 - 102
[48] Correction to: On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense
Manuel Ordóñez Cabrera
Andrew Rosalsky
Mehmet Ünver
Andrei Volodin
TEST, 2021, 30 : 1076 - 1077
[49] On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense (vol 30, pg 83, 2021)
Ordonez Cabrera, Manuel
Rosalsky, Andrew
Unver, Mehmet
Volodin, Andrei
TEST, 2021, 30 (04) : 1076 - 1077

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