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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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1978
Row sums \( \mathop \sum \nolimits_{i = 1}^{{k_n}} {X_{ni}} \) S of arrays of random variables {Xni1 ≤ i≤kn >→ ∞n ≥ 1} that are rowwise independent have been considered briefly with respect to the Marcinkiewicz–Zygmund type strong laws of large numbers (Example 10.4.1).
Yuan Shih Chow, Henry Teicher
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Row sums \( \mathop \sum \nolimits_{i = 1}^{{k_n}} {X_{ni}} \) S of arrays of random variables {Xni1 ≤ i≤kn >→ ∞n ≥ 1} that are rowwise independent have been considered briefly with respect to the Marcinkiewicz–Zygmund type strong laws of large numbers (Example 10.4.1).
Yuan Shih Chow, Henry Teicher
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Journal of Theoretical Probability, 1988
[For part I see Adv. Math. 69, No.1, 115-132 (1988; Zbl 0646.60017).] Let G be a commutative topological group which is separated by its continuous characters. Consider a triangular array of distributions on G with the property that its row-wise convolution products converge to a limit \(\mu\).
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[For part I see Adv. Math. 69, No.1, 115-132 (1988; Zbl 0646.60017).] Let G be a commutative topological group which is separated by its continuous characters. Consider a triangular array of distributions on G with the property that its row-wise convolution products converge to a limit \(\mu\).
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Infinitely Divisible Distributions
1975A distribution function F (x) and the corresponding c.f. f (t) are said to be infinitely divisible if for every positive integer n there exists a c.f. f n (t) such that $$f\left( t \right) = {\left( {{f_n}\left( t \right)} \right)^n}$$ (1.1)
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Infinitely Divisible Processes
2014In Chapter 11 we investigate infinitely divisible processes in a far more general setting than what mainstream probability theory has yet considered: we make no assumption of stationarity of increments of any kind and our processes are actually indexed by an abstract set.
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Infinitely Divisible Processes
2016Infinitely divisible stochastic processes form a broad family whose structure is reasonably well understood. A stochastic process \({\bigl (X(t),\,t \in T\bigr )}\) is said to be infinitely divisible if for every n = 1, 2, …, there is a stochastic process \(\bigl( Y(t),\, t\in T\bigr)\) such ...
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Infinitely divisible distributions in turbulence
Physical Review E, 1994The imbedding of the scale similarity of random fields into the theory of infinitely divisible probability distributions is considered. The general probability distribution for the breakdown coefficients of turbulent energy dissipation is obtained along with corresponding similarity exponents.
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