Abstract
The present paper deals with the problem of trajectory fitting estimation for nonlinear stochastic differential equations with reflection based on continuous-time observation. Under some regularity conditions, the consistency, the rate of convergence and the asymptotic distributions of the trajectory fitting estimator are discussed by using Skorohod equation, Toeplitz lemma and the strong law of large numbers.
Funding Statement
The Xuekang Zhang was supported by National Natural Science Foundation of China under Grant 12101004, the Natural Science Research Project of Anhui Educational Committee for Outstanding Youth Science Foundation under Grant 2023AH030021, and Research Fund for Anhui Provincial Talent Innovation Team under Grant 2023AH010011. The Guangjun Shen was supported in part by National Natural Science Foundation of China Grant 12071003.
Acknowledgments
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Xuekang Zhang. Guangjun Shen. "Trajectory fitting estimation for nonlinear stochastic differential equations with reflection." Braz. J. Probab. Stat. 38 (1) 177 - 191, March 2024. https://doi.org/10.1214/24-BJPS599
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