Spectral representations of quasi-infinitely divisible processes

Passeggeri, Riccardo

doi:10.1016/j.spa.2019.05.014

Cited by 17 publications

(75 citation statements)

References 22 publications

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“…This notion finds interesting applications in theory of stochastic processes (see [16] and [21]), number theory (see [20]), physics (see [6] and [7]), insurance mathematics (see [25]).…”

Section: Introductionmentioning

confidence: 99%

Spectral representations of characteristic functions of discrete probability laws

Alexeev¹,

Khartov²

2021

Preprint

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We consider discrete probability laws on the real line, whose characteristic functions are separated from zero. In particular, this class includes arbitrary discrete infinitely divisible laws and lattice probability laws, whose characteristic functions have no zeroes on the real line. We show that characteristic functions of such laws admit spectral Lévy-Khinchine type representations. We also apply the representations of such laws to obtain limit and compactness theorems with convergence in variation to probability laws from this class. Thus we generalize the corresponding results from the recent papers [11] and [17].

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“…This notion finds interesting applications in theory of stochastic processes (see [16] and [21]), number theory (see [20]), physics (see [6] and [7]), insurance mathematics (see [25]).…”

Section: Introductionmentioning

confidence: 99%

Spectral representations of characteristic functions of discrete probability laws

Alexeev¹,

Khartov²

2021

Preprint

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“…

In this work we present a family of quasi-infinitely divisible (QID) random measures and show that it is dense in the class of all independently scattered random measures under convergence in distribution. Further, we provide an extension of a classical measure theoretical result which enable us to generalise and unify some of the results on QID random measures in [15].

…”

mentioning

confidence: 95%

“…In [15], the QID framework is extended to real-valued random measures and stochastic processes. [15] represents the extension of the celebrated Rajput and Rosinski's 1989 paper [17] to the QID framework.…”

Section: Introductionmentioning

confidence: 99%

On quasi-infinitely divisible random measures

Passeggeri¹

2019

Preprint

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“…Recently, applications of quasi-infinitely divisible distributions have been found in physics (Demni and Mouayn [11], Chhaiba et al [8]) and insurance mathematics (Zhang et al [33]). Quasi-infinitely divisible processes and quasi-infinitely divisible random measures and integration theory with respect to them have been considered in Passeggieri [27]. Quasi-infinitely divisible distributions have also found applications in number theory, see e.g.…”

Section: Introductionmentioning

confidence: 99%

On multivariate quasi-infinitely divisible distributions

Berger¹,

Kutlu²,

Lindner³

2021

Preprint

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A quasi-infinitely divisible distribution on R d is a probability distribution µ on R d whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions on R d . Equivalently, it can be characterised as a probability distribution whose characteristic function has a Lévy-Khintchine type representation with a "signed Lévy measure", a so called quasi-Lévy measure, rather than a Lévy measure. A systematic study of such distributions in the univariate case has been carried out in Lindner, Pan and Sato [20]. The goal of the present paper is to collect some known results on multivariate quasiinfinitely divisible distributions and to extend some of the univariate results to the multivariate setting. In particular, conditions for weak convergence, moment and support properties are considered. A special emphasis is put on examples of such distributions and in particular on Z d -valued quasi-infinitely divisible distributions.

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Spectral representations of quasi-infinitely divisible processes

Cited by 17 publications

References 22 publications

Spectral representations of characteristic functions of discrete probability laws

Spectral representations of characteristic functions of discrete probability laws

On quasi-infinitely divisible random measures

On multivariate quasi-infinitely divisible distributions

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