Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also...

Sn = Xn1 + ... + Xnn has the same distribution F. The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de...

Gottfried Leibniz and Descartes discussed the infinite divisibility of extension. Actual divisibility may be limited due to unavailability of cutting...

=t-s} . The distribution of a Lévy process has the property of infinite divisibility: given any integer n, the law of a Lévy process at time t can be...

{\textstyle {\frac {\sigma ^{2}}{n}}} . This property is called infinite divisibility. Conversely, if X 1 {\textstyle X_{1}} and X 2 {\textstyle X_{2}}...

"Achilles Paradox", which illustrates the problematic concept of infinite divisibility in space and time. In this paradox, Zeno argues that a swift runner...

{\displaystyle \log(Z_{s})=\sum _{p\in {\mathcal {P}}}X(p^{-s})\,\log(p)} is infinitely divisible with Lévy measure given by the following sum of Dirac masses: Π s...

\in (0,2]} . The symmetric generalized Gaussian distribution is an infinitely divisible distribution if and only if β ∈ ( 0 , 1 ] ∪ { 2 } {\displaystyle...

distribution defined on N 0 {\displaystyle \mathbb {N} _{0}} is infinitely divisible, that is, for any positive integer n {\displaystyle n} , there exist...

parameters, see Mathai or Moschopoulos. The gamma distribution exhibits infinite divisibility. If X ∼ G a m m a ( α , θ ) , {\displaystyle X\sim \mathrm {Gamma}...

1061/(ASCE)0733-9429(1990)116:7(946). Thorin, Olof (1977). "On the infinite divisibility of the lognormal distribution". Scandinavian Actuarial Journal....

distribution, we write X ~ Exp(λ). The exponential distribution exhibits infinite divisibility. The cumulative distribution function is given by F ( x ; λ ) =...

affords a quick way to see that the negative binomial distribution is infinitely divisible. The following recurrence relations hold: For the probability mass...

Every infinitely divisible probability distribution is a limit of compound Poisson distributions. And compound Poisson distributions is infinitely divisible...

{\mu }{n}}+X_{i}-Y_{i}\right)\sim {\textrm {Laplace}}(\mu ,b)} (infinite divisibility) If X has a Laplace distribution, then Y = eX has a log-Laplace...

In probability theory, a degenerate distribution on a measure space ( E , A , μ ) {\displaystyle (E,{\mathcal {A}},\mu )} is a probability distribution...

In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus...

characterization of Poisson point process and infinite divisibility. Sato, Ken-Ito (1999). Lévy processes and infinitely divisible distributions. Cambridge University...

issues demanding proof and, e.g., Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered...

In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions...

physics. Physics portal Chemistry portal History of quantum mechanics Infinite divisibility Outline of chemistry Motion Timeline of atomic and subatomic physics...

In probability theory and statistics, the χ 2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution of...

famous treatment. In 1929, de Finetti introduced the concept of infinitely divisible probability distributions. He also introduced de Finetti diagrams...

Shalom (2006), "Divisible is injective", Soochow J. Math., 32 (2): 241–243, ISSN 0250-3255, MR 2238765 Griffith, Phillip A. (1970). Infinite Abelian group...

'to stand upon or near.' The continuous nature of time and its infinite divisibility was addressed by Aristotle in his Physics, where he wrote on Zeno's...

The Skellam distribution is the discrete probability distribution of the difference N 1 − N 2 {\displaystyle N_{1}-N_{2}} of two statistically independent...

(also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition...

the premise that substances are infinitely divisible and cannot have simple parts. Furthermore, each of their infinite parts determines every other part...

portfolio selection. A random variable Y {\displaystyle Y} is called infinitely divisible if, for each n = 1 , 2 , … {\displaystyle n=1,2,\dots } , there are...

ternary quadratic forms. Linnik obtained numerous results concerning infinitely divisible distributions. In particular, he proved the following generalisation...