Self-decomposable discrete distributions and branching processes

DOI10.1007/BF00537228zbMath0476.60016OpenAlexW3023729519MaRDI QIDQ3933693

K. van Harn, Wim Vervaat, F. W. Steutel

Publication date: 1982

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00537228

zbMATH Keywords

representation theoremscentral limit problemself-decomposable discrete distributions

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (24)

Count Data Time Series Models Based on Expectation Thinning ⋮ Stability equations for processes with stationary independent increments using branching processes and Poisson mixtures ⋮ On discrete \(\alpha\)-unimodality ⋮ Characterization of discrete laws via mixed sums and Markov branching processes ⋮ REGENERATIVE MUTATION PROCESSES RELATED TO THE SELFDECOMPOSABILITY OF SIBUYA DISTRIBUTIONS ⋮ ON LÉVY STABLE AND SEMISTABLE DISTRIBUTIONS ⋮ Taylor's law for some infinitely divisible probability distributions from population models ⋮ Discrete semistable probability distributions ⋮ On Mittag-Leffler distributions and related stochastic processes ⋮ Certain classes of discrete distributions in modeling risk control operations and establishing a transformation for probability generating functions ⋮ Stability for random measures, point processes and discrete semigroups ⋮ Discrete stable random variables ⋮ Finite thinning-selfdecomposable point processes ⋮ On new mechanisms leading to heavy-tailed distributions related to the ones of Yule-Simon ⋮ Integral part models in information systems and educational processes ⋮ Negative binomial time series models based on expectation thinning operators ⋮ Discrete semi-stable distributions ⋮ Semi-self-decomposable distributions on \(\mathbb Z_{+}\) ⋮ Scaling features of two special Markov chains involving total disasters ⋮ Remembering Wim Vervaat ⋮ Stability and self‐decomposability of semi‐group valued random variables ⋮ Scaled Sibuya distribution and discrete self-decomposability ⋮ Chance mechanisms involving Sibuya distribution and its relatives ⋮ Ergodicities and Exponential Ergodicities of Dawson--Watanabe Type Processes

Cites Work

• Discrete analogues of self-decomposability and stability
• Familles d'opérateurs potentiels
• Integer-valued branching processes with immigration
• A characterization of self-decomposable probabilities on the half-line
• A condition for absolute continuity of infinitely divisible distribution functions
• A characterization of potential kernels on the positive half-line
• The Limit of a Sequence of Branching Processes
• Continuous state branching processes
• Limit theorems for the Galton-Watson process with time-dependent immigration
• Regularly varying functions
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