We consider an indecomposable Galton-Watson branching process with a countable set of types. Assuming that the process is critical and may have infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behaviour of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types.

Bibliography: 20 titles.

中文翻译：

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具有可数类型集和无限二阶矩的临界 Galton-Watson 分支过程

我们认为与数集的类型不可分解高尔顿-Watson分枝过程。假设过程是关键的，并且可能有一些（或所有）类型的颗粒的后代大小的方差无穷我们描述的方法的生存概率的渐近行为和建立Yaglom型条件极限定理无限维所有类型的颗粒的数目的向量。

参考书目：20个标题。