http://hdl.handle.net/20.500.12128/8799
Title: | Weak law of large numbers for iterates of random-valued functions |
Authors: | Baron, Karol |
Keywords: | Random-valued functions; Iterates; Weak law of large numbers; Convergence in law; Convergence in probability |
Issue Date: | 2019 |
Citation: | Aequationes Mathematicae, Vol. 93, no. 2 (2019), s. 415-423 |
Abstract: | Given a probability space (Ω,A, P), a complete and separable metric space X with the σ-algebra B of all its Borel subsets and a B⊗A-measurable f : X ×Ω → X we consider its iterates fn defined on X × ΩN by f0(x, ω) = x and fn(x, ω) = f fn−1(x, ω), ωn for n ∈ N and provide a simple criterion for the existence of a probability Borel measure π on X such that for every x ∈ X and for every Lipschitz and bounded ψ : X → R the sequence 1 n n−1 k=0 ψ fk(x, ·) n∈N converges in probability to X ψ(y)π(dy). |
URI: | http://hdl.handle.net/20.500.12128/8799 |
DOI: | 10.1007/s00010-018-0585-0 |
ISSN: | 1420-8903 0001-9054 |
Appears in Collections: | Artykuły (WNŚiT) |
File | Description | Size | Format | |
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Baron_Weak_law_of_large_numbers_for_iterates.pdf | 457,09 kB | Adobe PDF | View/Open |
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