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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.07797 |
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| _version_ | 1866917388689080320 |
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| author | Zheng, Chao Pan, Jiangtao Wang, Qun |
| author_facet | Zheng, Chao Pan, Jiangtao Wang, Qun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07797 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm Zheng, Chao Pan, Jiangtao Wang, Qun Statistics Theory Optimization and Control Probability 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. |
| title | Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm |
| topic | Statistics Theory Optimization and Control Probability |
| url | https://arxiv.org/abs/2304.07797 |