带有周期漂移自排斥扩散的最小二乘估计
Least Squares Estimation fora Self-Repelling Di?usion withPeriodic Drift
摘要: 本文研究一类由标准布朗运动驱动且带有周期漂移的自排斥扩散模型，若 θ为未知的自排斥参数， L(t)为周期的参数函数，本文的主要目的是讨论当 θ> 0时参数的估计问题。利用 L(t)的周期性与 Frobenius矩阵公式，我们建立了参数的最小二乘估计量，并进一步讨论了该估计量的相合性与渐近分布等渐近行为。
Abstract: In this paper, we consider a self-repelling diffusion model with periodic drift: L(t) is a periodic, parametric function; θ is unknown parameter. The main object of this paper is to study the estimation problem of the parameters when θ> 0. By utilizing the periodicity of L(t) and the Frobenius matrix formula, we have established the least squares estimator of parameters, and we have discussed the asymptotic behavior of the estimator.
文章引用：俞乐梵, 田琳琳, 闫理坦. 带有周期漂移自排斥扩散的最小二乘估计[J]. 统计学与应用, 2026, 15(5): 208-225. https://doi.org/10.12677/SA.2026.155120

参考文献

[1] Durrett, R.T. and Rogers, L.C.G. (1992) Asymptotic Behavior of Brownian Polymers. Probability Theory and Related Fields, 92, 337-349. [Google Scholar] [CrossRef] 
[2] Pemantle, R. (1988) Phase Transition in Reinforced Random Walk and RWRE on Trees. The Annals of Probability, 16, 1229-1241. [Google Scholar] [CrossRef] 
[3] Coppersmith, D. and Diaconis, P. (1986) Random Walks with Reinforcement. Unpublished Manuscript.
[4] Benaïm, M., Ledoux, M. and Raimond, O. (2002) Self-Interacting Diffusions. Probability Theory and Related Fields, 122, 1-41. [Google Scholar] [CrossRef] 
[5] Chakravarti, N. and Sebastian, K.L. (1997) Fractional Brownian Motion Models for Polymers. Chemical Physics Letters, 267, 9-13. [Google Scholar] [CrossRef] 
[6] Cherayil, B.J. and Biswas, P. (1993) Path Integral Description of Polymers Using Fractional Brownian Walks. The Journal of Chemical Physics, 99, 9230-9236.[CrossRef] 
[7] Yan, L., Sun, Y. and Lu, Y. (2007) On the Linear Fractional Self-Attracting Diffusion. Journal of Theoretical Probability, 21, 502-516. [Google Scholar] [CrossRef] 
[8] Berzin, C., Latour, A. and Leon, J.R. (2014) Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion. Springer. [Google Scholar] [CrossRef] 
[9] Es-Sebaiy, K. (2013) Berry-Esséen Bounds for the Least Squares Estimator for Discretely Observed Fractional Ornstein-Uhlenbeck Processes. Statistics & Probability Letters, 83, 2372- 2385.[CrossRef] 
[10] Es-Sebaiy, K. and Nourdin, I. (2013) Parameter Estimation for Α-Fractional Bridges. In: Viens, F., Feng, J., Hu, Y. and Nualart, E., Eds., Malliavin Calculus and Stochastic Analysis, Springer, 385-412. [Google Scholar] [CrossRef] 
[11] Hu, Y. and Nualart, D. (2010) Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes. Statistics & Probability Letters, 80, 1030-1038. [Google Scholar] [CrossRef] 
[12] Kleptsyna, M.L. and Le Breton, A. (2002) Statistical Analysis of the Fractional OrnsteinUhlenbeck Type Process. Statistical Inference for Stochastic Processes, 5, 229-248. [Google Scholar] [CrossRef] 
[13] Prakasa Rao, B.L.S. (2010) Statistical Inference for Fractional Diffusion Processes. John Wiley and Sons Ltd.
[14] Dehling, H., Franke, B. and Kott, T. (2010) Drift Estimation for a Periodic Mean Reversion Process. Statistical Inference for Stochastic Processes, 13, 175-192.[CrossRef] 
[15] Kuo, H.H. (2006) Introduction to Stochastic Integration. Springer
[16] Itô, K. (1944) Stochastic Integral. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 20, 519-524. [Google Scholar] [CrossRef] 
[17] Hu, Y., Nualart, D. and Zhou, H. (2017) Parameter Estimation for Fractional OrnsteinUhlenbeck Processes of General Hurst Parameter. Statistical Inference for Stochastic Processes, 22, 111-142. [Google Scholar] [CrossRef] 
[18] Yaohong, G. and Litan, Y. (2018) Least Squares Estimation for a Linear Self-Repelling Diffusion Driven by Fractional Brownian Motion. Scientia Sinica Mathematica, 48, 1143-1158. [Google Scholar] [CrossRef] 

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