Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm
Abstract
The randomized unbiased estimators of Rhee and Glynn (Operations Research:63(5), 1026-1043, 2015) can be highly efficient at approximating expectations of path functionals associated with stochastic differential equations (SDEs). However, there is a lack of algorithms for calculating the optimal distributions with an infinite horizon. In this article, based on the method of Cui et.al. (Operations Research Letters: 477-484, 2021), we prove that, under mild assumptions, there is a simple representation of the optimal distributions. Then, we develop an adaptive algorithm to compute the optimal distributions with an infinite horizon, which requires only a small amount of computational time in prior estimation. Finally, we provide numerical results to illustrate the efficiency of our adaptive algorithm.
Cite
@article{arxiv.2304.07797,
title = {Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm},
author = {Chao Zheng and Jiangtao Pan and Qun Wang},
journal= {arXiv preprint arXiv:2304.07797},
year = {2026}
}