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arXiv · 2304.07797

Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm

Chao Zheng·Jiangtao Pan·Qun Wang
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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.

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BibTeXRIS

Chao Zheng, Jiangtao Pan, Qun Wang. 2023-04-16. Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm. https://doi.org/10.1093/imanum%2Fdraf017

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