Results 11 to 20 of about 854 (209)
Sparsity and Infinite Divisibility [PDF]
IEEE Transactions on Information Theory, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arash Amini, Michael Unser
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Infinite Divisibility of Information [PDF]
IEEE Transactions on Information Theory, 2021 We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if, for any $n\ge1$, there exists an i.i.d.
Li, Cheuk Ting
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On the infinite divisibility of distributions of some inverse subordinators
Modern Stochastics: Theory and Applications, 2018 We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely divisible.
Arun Kumar, Erkan Nane
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A General Result on Infinite Divisibility
Annals of Probability, 1979 Using and refining a technique developed by O. Thorin, we prove: THEOREM. Let $f(x) = C\cdot x^{\beta - 1} h(x), x > 0$, be a probability density on $(0, \infty)$. Here $\beta > 0$ and $h$ is continuous and satisfies $h(0) = 1$. Assume that $h$ can be analytically continued to the whole complex plane cut along the negative real axis and assume that $h$
Lennart Bondesson
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Infinite Divisibility in Stochastic Processes
Annals of Probability, 1979 It is shown that infinite divisibility of random variables, such as first passage times in a stochastic process, is often connected with the existence of an imbedded terminating renewal process. The idea is used to prove that for a continuous time Markov chain with two, three or four states all first passage times are infinitely divisible but for more ...
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Mutant Number Laws and Infinite Divisibility
Axioms, 2022 Concepts of infinitely divisible distributions are reviewed and applied to mutant number distributions derived from the Lea-Coulson and other models which describe the Luria-Delbrück fluctuation test.
Anthony G. Pakes
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The life and work of Olof Thorin (1912–2004); pp. 18–25 [PDF]
Proceedings of the Estonian Academy of Sciences, 2008 This paper reviews Olof Thorinâs contributions to mathematical analysis, actuarial mathematics, and probability theory, though in reversed order. In probability theory he is known for his path-breaking work on infinite divisibility.
Lennart Bondesson +2 more
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On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums
Mathematics, 2021 We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in ...
Irina Shevtsova, Mikhail Tselishchev
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On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos
Modern Stochastics: Theory and Applications, 2020 Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility are presented as well as more easily verifiable sufficient conditions.
Andreas Basse-O’Connor +2 more
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On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families
Mathematics, 2021 Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
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