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Free infinite divisibility for beta distributions and related ones [PDF]

Electronic Journal of Probability, 2014
We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions.
Takahiro Hasebe
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On the Infinite Divisibility of Polynomials in Infinitely Divisible Random Variables

1992
It is shown that all second degree polynomials in standard normal random variables are infinitely divisible and an example of a polynomial of degree three or more is given which is not infinitely divisible. It is also shown that if a polynomial in a random variable with support {0,1,2,…} is infinitely divisible then it must be linear.
V. K. Rohatgi, G. J. Székely
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On Indecomposable Laws with Infinitely Divisible Projections

Theory of Probability & Its Applications, 1985
For any \(n\geq 2\) the authors construct the n-dimensional indecomposable distributions whose all one-dimensional projections are infinitely divisible. A somewhat stronger result in which the infinite divisibility of the projections on all subspaces of all dimensions \(1\leq k\leq n-1\) is guaranteed was obtained independently in the paper by \textit ...
Ushakov, V. G., Ushakov, N. G.
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Testing Max-Infinite Divisibility

Theory of Probability & Its Applications, 1993
See the review in Zbl 0753.62036.
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Convolution equivalence and infinite divisibility

Journal of Applied Probability, 2004
Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
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The Case for Infinite Divisibility

2004
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Infinitely divisible distributions in turbulence

Physical Review E, 1994
The 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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Infinitely divisible sequences

Scandinavian Actuarial Journal, 1978
Abstract 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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On Infinite Divisibility of Convolution and Mapping Kernels

Fundamenta Informaticae, 2017
Determining whether convolution and mapping kernels are always infinitely divisible has been an unsolved problem. The mapping kernel is an important class of kernels and is a generalization of the well-known convolution kernel. The mapping kernel has a wide range of application. In fact, most of kernels known in the literature for discrete data such as
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Infinitely Divisible Distributions

2014
For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma ...
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