Metric diophantine approximation and probability.
Hensley, Doug (1998)
The New York Journal of Mathematics [electronic only]
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Hensley, Doug (1998)
The New York Journal of Mathematics [electronic only]
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Charles M. Stein (1985)
Banach Center Publications
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A Milian (1991)
Applicationes Mathematicae
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Pavla Kunderová (1978)
Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika
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Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Alexander R. Pruss (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false...
P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2011)
RAIRO - Operations Research
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In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension . We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach...
J. Łąski (1976)
Applicationes Mathematicae
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C. V. Stanojević (1973)
Recherche Coopérative sur Programme n°25
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B. Schmitt (1989)
Banach Center Publications
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Tomoki Inoue (1992)
Annales Polonici Mathematici
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We study the asymptotic stability of densities for piecewise convex maps with flat bottoms or a neutral fixed point. Our main result is an improvement of Lasota and Yorke's result ([5], Theorem 4).
Mostafa K. Ardakani, Shaun S. Wulff (2014)
Discussiones Mathematicae Probability and Statistics
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Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...
Anthony Quas (1999)
Studia Mathematica
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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for or expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Neil Dobbs, Bartłomiej Skorulski (2008)
Fundamenta Mathematicae
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We show that for entire maps of the form z ↦ λexp(z) such that the orbit of zero is bounded and Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.