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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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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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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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Infinitely Divisible Point Processes.

Journal of the Royal Statistical Society. Series A (General), 1979
Alan F. Karr, K. Matthes, J. Kerstan, J. Mecke   +3 more
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Infinitely divisible stochastic processes

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1967
It often happens that a stochastic process may be approximated by a sum of a large number of independent components no one of which contributes a significant proportion of the whole. For example the depth of water in a lake with many small rivers flowing into it from distant sources, or the point process of calls entering a telephone exchange ...
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Infinitely Divisible Processes

Theory of Probability & Its Applications, 1970
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Infinite Divisibility

2009
Bjørn Sundt, Raluca Vernic
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On Infinitely Divisible Distributions

Theory of Probability & Its Applications, 1975
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Infinitely divisible processes

2002
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Infinitely Divisible Laws

2010
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