Theory of Probability &Its Applications, Volume 67, Issue 1, Page 141-153, May 2022.
This article is an essay, both expository and argumentative, on the Galton--Watson process as a tool in the domain of branching processes. It is at the same time the author's way of honoring two distinguished scientists in this domain, both from the Russian Academy of Sciences, and congratulating them on their special birthdays. The thread of the article is the role which the Galton--Watson process had played in the author's own research. We start with a discussion on a controlled Galton--Watson process. Then we pass to random absorbing processes, and also recall and discuss a problem in medicine. Further questions bring us, via the Borel--Cantelli lemma, to $\varphi$-branching processes and extensions. To gain more generality we then look at bisexual Galton--Watson processes. Finally, we briefly discuss relatively complicated resource-dependent branching processes to show that, again, using Galton--Watson reproduction schemes (whenever reasonable) can be a convincing approach to new processes, which are then sufficiently tractable to obtain results of interest.

中文翻译：

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Galton--Watson 过程及其作为分支过程构建块的作用

概率论及其应用，第 67 卷，第 1 期，第 141-153 页，2022 年 5 月。
本文是一篇关于高尔顿-沃森过程作为分支过程领域工具的说明性和论证性文章。同时，作者也以此向两位来自俄罗斯科学院的杰出科学家致敬，并祝贺他们的特殊生日。文章的主线是高尔顿-沃森过程在作者自己的研究中所起的作用。我们首先讨论受控的高尔顿-沃森过程。然后我们进入随机吸收过程，并回忆和讨论医学中的一个问题。进一步的问题通过 Borel--Cantelli 引理将我们带到 $\varphi$-分支过程和扩展。为了获得更多的普遍性，我们接着看双性恋的高尔顿-沃森过程。最后，