Convergence of the population dynamics algorithm in the Wasserstein metric

Abstract

We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the special endogenous solution to a variety of branching stochastic fixed-point equations, including the smoothing transform, the high-order Lindley equation, the discounted tree-sum and the free-entropy equation. Specifically, we show its convergence in the Wasserstein metric of order $p$ ($p \geq 1$) and prove the consistency of estimators based on the sample pool produced by the algorithm.