Structural, continuity, and asymptotic properties of a branching particle system

DOI10.1007/s10986-009-9049-5zbMath1189.60157OpenAlexW2081007011MaRDI QIDQ1033570

Vladimir V. Vinogradov, Kenneth J. Hochberg

Publication date: 6 November 2009

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-009-9049-5

zbMATH Keywords

asymptotic expansionLaplace methodLévy processBessel functionlocal limit theoremPoisson mixtureDawson-Watanabe superprocessEsscher transformcluster structureunit variance functionBabel classAthreya-Ney-type representationbirth-death Markov processbranching-diffusing particle systemcontinuity of stochastic process in mean squareJørgensen-type convergenceleading error termPoisson-exponential lawPólya-Aeppli lawpower-variance familysummation invarianceYaglom-type exponential limit lawzero-modified geometric law

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Asymptotic distribution theory in statistics (62E20) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Diffusion processes (60J60) Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (4)

The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processes ⋮ Domains of attraction to Tweedie distributions ⋮ New properties and representations for members of the power-variance family. II ⋮ New properties and representations for members of the power-variance family. I

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