Abstract The weighted branching process is a natural extension of branching processes. Branching processes count only individuals, weighted branching processes give every individual an abstract weight. Mathematically, we face a (random) dynamical system indexed by a tree. We give an overview of research into this directions, including and unifying many examples of this structure, like Biggins branching random walk and Mandelbrot cascades. WBP are closely connected to stochastic fixed-point equations, fractals and have many applications in genetics, computer science and algorithms. The most advanced example we present is the Quicksort process.

中文翻译：

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随机定点方程

摘要 加权分支过程是分支过程的自然延伸。分支过程只计算个体，加权分支过程赋予每个个体一个抽象权重。在数学上，我们面临一个由树索引的（随机）动力系统。我们概述了对该方向的研究，包括并统一了这种结构的许多示例，例如 Biggins 分支随机游走和 Mandelbrot 级联。WBP 与随机定点方程、分形密切相关，在遗传学、计算机科学和算法中有许多应用。我们展示的最高级的例子是快速排序过程。