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Some criteria of rational-infinite divisibility for probability laws
Electronic Journal of Probability, 2023We study the class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$.
Alexey Khartov
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A Cramér–Wold device for infinite divisibility of Zd-valued distributions
Bernoulli, 2022We show that a Cramér–Wold device holds for infinite divisibility of Zd-valued distributions, i.e. that the distribution of a Zd-valued random vector X is infinitely divisible if and only if the distribution of aTX is infinitely divisible for all a ∈ Rd,
David Berger, Alexandra H Lindner
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Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions
Complex Analysis and Operator Theory, 2020We consider weighted shift operators having the property of moment infinite divisibility; that is, for any p>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
C. Benhida, R. Curto, G. Exner
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Infinitely divisible sequences
Scandinavian Actuarial Journal, 1978Abstract Sequences and related by the system of equations occur frequently in a number of areas of mathematics, and when they do one is often interested in relating the asymptotic behaviours of the two sequences. In probability theory sequences n , which arise when one has the added conditions b0 > 0 and aj⩾ 0, often occur.
John Hawkes, John D. Jenkins
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Testing Max-Infinite Divisibility
Theory of Probability & Its Applications, 1993See the review in Zbl 0753.62036.
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Journal of Applied Probability, 1977
Necessary and sufficient conditions are given for a distribution function in ℝ2 to be max-infinitely divisible. The d.f. F is max i.d. if F t is a d.f. for every t > 0. This property is essential in defining multivariate extremal processes and arises in an approach to the study of the range of an i.i.d. sample.
Balkema, A. A., Resnick, S. I.
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Necessary and sufficient conditions are given for a distribution function in ℝ2 to be max-infinitely divisible. The d.f. F is max i.d. if F t is a d.f. for every t > 0. This property is essential in defining multivariate extremal processes and arises in an approach to the study of the range of an i.i.d. sample.
Balkema, A. A., Resnick, S. I.
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The American Mathematical Monthly, 2006
Assembling natural numbers in such nice patterns often has interesting consequences, and so it is in this case. Each of the aforementioned matrices is endowed with positive definiteness of a very high order: for every positive real number r the matrices with entries a\-, b\-, c\-, and d\are positive semidefinite.
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Assembling natural numbers in such nice patterns often has interesting consequences, and so it is in this case. Each of the aforementioned matrices is endowed with positive definiteness of a very high order: for every positive real number r the matrices with entries a\-, b\-, c\-, and d\are positive semidefinite.
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A criterion of quasi-infinite divisibility for discrete laws
Statistics and Probability Letters, 2021A. Khartov
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