Efficient simulation for branching linear recursions

We provide an algorithm for simulating the unique attracting fixed-point of linear branching distributional equations. Such equations appear in the analysis of information ranking algorithms, e.g., PageRank, and in the complexity analysis of divide and conquer algorithms, e.g., Quicksort. The naive simulation approach would be to simulate exactly a suitable number of generations of a weighted branching process, which has exponential complexity in the number of generations being sampled. Instead, we propose an iterative bootstrap algorithm that has linear complexity; we prove its convergence and the consistency of a family of estimators based on our approach.