Abstract

This article presents a brief on using a saddlepoint approximations technique to solve some branching process problems; this method of approximation provides a good understanding of branching process behaviors such as probability density, mass function, and cumulative distribution function based on a moment generating function for complicated models such as nuclear chain reaction, survival of family name problems, and extinction probability problem.

中文翻译：

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修改的分支过程和鞍点近似

摘要

本文简要介绍了使用鞍点近似技术来解决一些分支过程问题。这种近似方法基于矩量生成函数的复杂模型（例如核链反应，姓氏问题的生存和灭绝概率问题），基于矩生成函数，很好地理解了分支过程的行为，例如概率密度，质量函数和累积分布函数。