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Discrete Semi-Self-Decomposability Induced by Semigroups

   
@article{EJP890,
	author = {Nadjib Bouzar},
	title = {Discrete Semi-Self-Decomposability Induced by Semigroups},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {composition semigroups, discrete distributions, infinite divisibility, semi-stability, Markov branching processes, weak convergence.},
	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.},
	pages = {no. 39, 1117-1133},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-890},    
        url = {http://ejp.ejpecp.org/article/view/890}}