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A note on infinitely divisible distribution on function fields [PDF]
Mathematica MoravicaIn this note, we define a function associated with the zeta function on function fields of genus g over a finite field Fq. We shown that the exponential of this function is the characteristic function of an infinitely divisible distribution on the real ...
Khmiri Jawher
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A direct approach to the stable distributions [PDF]
, 2016 The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general L\'evy-Khintchine ...
Pitman, E. J. G., Pitman, Jim
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Logarithmic Lévy process directed by Poisson subordinator
Modern Stochastics: Theory and Applications, 2019 Let $\{L(t),t\ge 0\}$ be a Lévy process with representative random variable $L(1)$ defined by the infinitely divisible logarithmic series distribution. We study here the transition probability and Lévy measure of this process.
Penka Mayster, Assen Tchorbadjieff
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On the infinite divisibility of inverse Beta distributions
Bernoulli, 2015 We show that all negative powers B_{a,b}^-{s} of the Beta distribution are infinitely divisible. The case b<1 follows by complete monotonicity, the case b > 1, s > 1 by hyperbolically complete monotonicity and the case b > 1, s < 1 by a Lévy perpetuity argument involving the hypergeometric series.
Bosch, Pierre, Simon, Thomas
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A New Decomposition of Infinitely Divisible Distributions
The Annals of Probability, 1975 In this paper, it is shown that a random variable $Z$ having an infinitely divisible distribution with a finite left extremity can be decomposed in distribution as the sum of two random variables such that, given one, the other has an infinitely divisible distribution of prescribed type.
Shanbhag, D. N., Gani, J.
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Volatility smile at the Russian option market
Journal of Business Economics and Management, 2006 The main derivative exchange in Russia is FORTS (Futures and Options in RTS) which is a division of Russian Trade System (RTS). The underlying assets of option contracts are futures on Russian companies’ shares: OJSC “EES"1, OJPC “Lukoil"2 and OJSC ...
D. Golembiovsky, I. Baryshnikov
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Infinite Divisibility in Euclidean Quantum Mechanics
, 2006 In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible.
B Finetti De +4 more
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The effect of random scale changes on limits of infinitesimal systems
International Journal of Mathematics and Mathematical Sciences, 1978 Suppose S={{Xnj, j=1,2,…,kn}} is an infinitesimal system of random variables whose centered sums converge in law to a (necessarily infinitely divisible) distribution with Levy representation determined by the triple (γ,σ2,M).
Patrick L. Brockett
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Intermittency of trawl processes [PDF]
, 2017 We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the dependence structure.
Grahovac, Danijel +2 more
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On quasi-infinitely divisible distributions [PDF]
Transactions of the American Mathematical Society, 2018 A quasi-infinitely divisible distribution on $\mathbb{R}$ is a probability distribution whose characteristic function allows a Lévy-Khintchine type representation with a "signed Lévy measure", rather than a Lévy measure. Quasi-infinitely divisible distributions appear naturally in the factorization of infinitely divisible distributions.
Lindner, Alexander +2 more
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