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Discrete Semi-Self-Decomposability Induced by Semigroups


 
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1. Title Title of document Discrete Semi-Self-Decomposability Induced by Semigroups
 
2. Creator Author's name, affiliation, country Nadjib Bouzar; University of Indianapolis; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) composition semigroups, discrete distributions, infinite divisibility, semi-stability, Markov branching processes, weak convergence.
 
3. Subject Subject classification Primary 60E07; Secondary 60F05.
 
4. Description Abstract A continuous semigroup of probability generating functions $\mathcal{F}:=(F_t, t\ge 0)$ is used to introduce a notion of discrete semi-selfdecomposability, or $\mathcal{F}$-semi-selfdecomposability, for distributions with support on $\bf Z_+$. $\mathcal{F}$-semi-selfdecomposable distributions are infinitely divisible and are characterized by the absolute monotonicity of a specific function. The class of $\mathcal{F}$-semi-selfdecomposable laws is shown to contain the $\mathcal{F}$- semistable distributions and the geometric $\mathcal{F}$-semistable distributions. A generalization of discrete random stability is also explored.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-06-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/890
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-890
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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