Abstract
We establish a Berry-Esseen theorem for random walks conditioned to stay positive under (the probability by Doob’s h-transform), which quantifies the convergence rate in the Kolmogorov distance of the central limit theorem proved by Bryn-Jones and Doney (2006). Our approach is based on a recent analogous result by Grama and Xiao (2021) for random walks conditioned to stay positive over a finite time interval.
Funding Statement
This work was supported in part by NSFC (No. 11971062) and the National Key Research and Development Program of China (No. 2020YFA0712900).
Acknowledgments
We are grateful to the anonymous referees for their careful reading and valuable suggestions that have improved the paper. In particular, we are deeply thankful to the referees for pointing out a gap in the original version of the manuscript and providing an idea to simplify the proof of Theorem 1.2.
Citation
Wenming Hong. Mingyang Sun. "Berry-Esseen theorem for random walks conditioned to stay positive." Electron. Commun. Probab. 29 1 - 8, 2024. https://doi.org/10.1214/24-ECP605
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