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dc.contributor.authorBaron, Karol-
dc.identifier.citationAequationes Mathematicae, 05 April 2019pl_PL
dc.description.abstractGiven a probability space (Ω,A, P), a complete and separable metric space X with the σ-algebra B of all its Borel subsets, a B ⊗A-measurable and contractive in mean f : X × Ω → X, and a Lipschitz F mapping X into a separable Banach space Y we characterize the solvability of the equation ϕ(x) = Ω ϕ (f(x, ω)) P(dω) + F(x) in the class of Lipschitz functions ϕ : X → Y with the aid of the weak limit πf of the sequence of iterates (fn(x, ·))n∈N of f, defined on X × ΩN by f0(x, ω) = x and fn(x, ω) = f fn−1(x, ω), ωn for n ∈ N, and propose a characterization of πf for some special rvfunctions in Hilbert spaces.pl_PL
dc.rightsUznanie autorstwa 3.0 Polska*
dc.subjectRandom-valued functionspl_PL
dc.subjectWeak limitpl_PL
dc.subjectIterative equationspl_PL
dc.subjectLipschitzian solutionspl_PL
dc.subjectBochner integralpl_PL
dc.subjectGaussian measurespl_PL
dc.titleWeak limit of iterates of some random-valued functions and its applicationpl_PL
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