Moment problems related to Bernstein functions

Simon, Thomas

doi:10.5802/afst.1640

Cited by 3 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The implication (44) was also observed [43, Proposition 1.16] and the proof there is based on an induction on n, without formalizing the class M n .…”

Section: Comments On the Factorizationsmentioning

confidence: 75%

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Jedidi¹,

Jurek²,

Al³

2021

Preprint

View full text Add to dashboard Cite

Inspirations for this paper can be traced to Urbanik [48] where convolution semigroups of multiple decomposable distributions were introduced. In particular, the classical gamma G t and log G t , t > 0 variables are selfdecomposable. In fact, we show that log G t is twice selfdecomposable if, and only if, t ≥ t 1 ≈ 0.15165. Moreover, we provide several new factorizations of the Gamma function and the Gamma distributions. To this end, we revisit the class of multiply selfdecomposable distributions, denoted L n (R), and propose handy tools for its characterization, mainly based on the Mellin-Euler's differential operator. Furthermore, we also give a perspective of generalization of the class L n (R) based on linear operators or on stochastic integral representations.

show abstract

“…The implication (44) was also observed [43, Proposition 1.16] and the proof there is based on an induction on n, without formalizing the class M n .…”

Section: Comments On the Factorizationsmentioning

confidence: 75%

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Jedidi¹,

Jurek²,

Al³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The asymptotics of Theorem 3 show that Xα,γ has integer moments of arbitrary order, positive or negative, and it is a natural question whether these integer moments characterize the law of Xα,γ , in other words whether Xα,γ or X−1 α,γ is M −det. This question was addressed in Proposition 4.1 of our previous paper [19], in the framework of generalized stable random variables.…”

Section: Introductionmentioning

confidence: 98%

“…The log-concavity also immediately implies Theorem 3 (a). For X α,γ , the log-concavity argument is no more valid and we use the alternative property that log X α,γ is self-decomposable, which implies an extended Lin's property as observed in [19].…”

Section: Introductionmentioning

confidence: 99%

A note on the $α-$Sun distribution

Simon¹

2023

Preprint

View full text Add to dashboard Cite

We investigate the analytical properties of the α−Sun random variable, which arises from the domain of attraction of certain storage models involving a maximum and a sum. In the Fréchet case we show that this random variable is infinitely divisible, and we give the exact behaviour of the density at zero. In the Weibull case we give the exact behaviour of the density at infinity, and we show that the behaviour at zero is neither polynomial nor exponential. This answers the open questions in the recent paper [21].

show abstract

A note on the α-Sun distribution

Simon

2023

Electron. Commun. Probab.

View full text Add to dashboard Cite

Moment problems related to Bernstein functions

Cited by 3 publications

References 25 publications

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

A note on the $α-$Sun distribution

A note on the α-Sun distribution

Contact Info

Product

Resources

About