A remarkable property of generalized gamma convolutions

Bondesson, Lennart

doi:10.1007/bf00334198

Cited by 10 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The class GGC of distributions appeared in Thorin's work and it includes popular models like log-normal distributions, Pareto distributions, and all positive stable random variables. They are closed in weak limits, addition of independent random variables, and multiplication of independent random variables, see [2] for further details.…”

Section: Weak Convergence Within Ggcmentioning

confidence: 99%

“…Before we start our discussions, we first write down the definition of GGC random variables, see [2,5] for more details. Definition 2.1.…”

Section: Weak Convergence Within Ggcmentioning

confidence: 99%

“…Proof. All nondegenerate random variables in GGC have probability density functions and they are unimodel, see part vi) of [2] for this (also see the introduction of [18]). Then the claim follows from [15] (also see page 383 of [13]).…”

Section: Robustness Of the Exponential Utility Maximizing Portfoliomentioning

confidence: 99%

See 2 more Smart Citations

Weak Convergence and Weak Convergence

Narita

Shidama

Endou

2015

Formalized Mathematics

View full text Add to dashboard Cite

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18], we regarded sequences of real numbers as sequences of RNS_Real. So we proved the last theorem in this section using the theorem (8) from [25]. In Section 3, we defined weak sequential compactness of real normed spaces. We showed some lemmas for the proof and proved the theorem of weak sequential compactness of reflexive real Banach spaces. We referred to [36], [23], [24] and [3] in the formalization.

show abstract

Section: Weak Convergence Within Ggcmentioning

confidence: 99%

“…Before we start our discussions, we first write down the definition of GGC random variables, see [2,5] for more details. Definition 2.1.…”

Section: Weak Convergence Within Ggcmentioning

confidence: 99%

See 1 more Smart Citation

Weak Convergence and Weak Convergence

Narita

Shidama

Endou

2015

Formalized Mathematics

View full text Add to dashboard Cite

show abstract

“…Moreover, all (probability) densities on (0, oo) which are limits of densities ( Cox (1981). A survey of the known properties of F and ~ can be found in Bondesson (1988).…”

Section: Introductionmentioning

confidence: 99%