What question did this study set out to answer?

To establish an extension of the Bingham-Doney theorem connecting initial offspring distribution and limit random variables in supercritical Galton-Watson branching processes.

March 1, 1982Journal of Applied Probability

On a theorem of bingham and doney

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To establish an extension of the Bingham-Doney theorem connecting initial offspring distribution and limit random variables in supercritical Galton-Watson branching processes.
Analyzed the probability distributions of the first-generation random variable Z1 and the martingale limit variable W in supercritical Galton-Watson processes.
Evaluated asymptotic tail behavior using the mathematical framework of regular variation for integer parameter values where α > 1.
Proved that regular variation in the distribution of Z1 is strictly equivalent to regular variation in the tail distribution of W for integer values of α > 1.
Extended classical branching process theory by resolving the two-way asymptotic relationship between initial family size and long-term population limits.

Implication

Theoretical analysis demonstrates equivalence between offspring distribution and limit tail variation in Galton-Watson processes, expanding classical probability theorems.

Abstract

We obtain an extension of a theorem of Bingham and Doney connecting the random variables Z 1 and W in the supercritical Galton-Watson process. The regular variation of the distribution of Z1 is equivalent to the regular variation of the tail of the distribution of W for integer values of α > 1.

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Cite This Study

Anne‐Marie De Meyer (1982) studied this question.

synapsesocial.com/papers/6a9a1d1e905266c79617c4c2 https://doi.org/10.1017/s0021900200028436

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Implication

Theoretical analysis demonstrates equivalence between offspring distribution and limit tail variation in Galton-Watson processes, expanding classical probability theorems.

On a theorem of bingham and doney

Key Points

Implication

Abstract

Discussion

Cite This Study

On a theorem of bingham and doney

Key Points

Implication

Abstract

Discussion

Cite This Study

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