由α-稳定过程驱动的线性自排斥扩散过程的参数估计
Parameter Estimation for the Linear Self-Repelling Diffusion Driven by α-Stable Motions
摘要: 本文研究如下线性自排斥扩散的参数估计问题：，其中，Mα是一个对称α-稳定过程(1＜α＜2)。该过程为一类自排斥扩散的类似过程。在连续观测条件下，我们使用最小二乘法对两个未知参数进行了估计，研究了它们的渐近分布，并通过仿真模拟探究了估计量的精度。
Abstract: In this paper, we consider parameter estimations of the linear self-repelling diffusion , where Mα is a symmetrical α-stable motion (1＜α＜2). The process is an analogue of the self-repelling diffusion. By using least squares method, we study estimators of unknown parameters, give their asymptotic distributions under the continuous observation and study the accuracy of the estimator.
文章引用：沈乐怡, 童金英, 闫理坦. 由α-稳定过程驱动的线性自排斥扩散过程的参数估计[J]. 统计学与应用, 2021, 10(5): 770-777. https://doi.org/10.12677/SA.2021.105079

参考文献

[1] Durrett, R. and Rogers, L.C.G. (1992) Asymptotic Behavior of Brownian Polymer. Probability Theory and Related Fields, 92, 337-349.
[Google Scholar] [CrossRef] 
[2] Cranston, M. and Le Jan, Y. (1995) Self-Attracting Diffusion: Two Case Studies. Mathematische Annalen, 303, 87-93.
[Google Scholar] [CrossRef] 
[3] Benaïm, M., Ciotir, I. and Gauthier, C.-E. (2015) Self-Repelling Diffusions via an Infinite Dimensional Approach. Stochastic Partial Differential Equations: Analysis and Computations, 3, 506-530.
[Google Scholar] [CrossRef] 
[4] Benaïm, M., Ledoux, M. and Raimond, O. (2002) Self-Interacting Diffusions. Probability Theory and Related Fields, 122, 1-41.
[Google Scholar] [CrossRef] 
[5] Cranston, M. and Mountford, T.S. (1996) The Strong Law of Large Numbers for a Brownian Polymer. Annals of Probability, 24, 1300-1323.
[Google Scholar] [CrossRef] 
[6] Gauthier, C.-E. (2016) Self Attracting Diffusions on a Sphere and Application to a Periodic Case. Electronic Communications in Probability, 21, 1-12.
[Google Scholar] [CrossRef] 
[7] Herrmann, S. and Roynette, B. (2003) Boundedness and Convergence of Some Self-Attracting Diffusions. Mathematische Annalen, 325, 81-96.
[Google Scholar] [CrossRef] 
[8] Herrmann, S. and Scheutzow, M. (2004) Rate of Convergence of Some Self-Attracting Diffusions. Stochastic Processes and Their Applications, 111, 41-55.
[Google Scholar] [CrossRef] 
[9] Mountford, T. and Tarrès, P. (2008) An Asymptotic Result for Brownian Polymers. Annales de l’IHP Probabilités et Statistiques, 44, 29-46.
[Google Scholar] [CrossRef] 
[10] Sun, X. and Yan, L. (2020) A Convergence on the Linear Self-Interacting Diffusion Driven by α-Stable Motion, to Appear. Stochastics.
[Google Scholar] [CrossRef] 
[11] Li, Z. and Ma, C. (2015) Asymptotic Properties of Estimators in a Stable Cox-Ingersoll-Ross Model. Stochastic Processes and Their Applications, 125, 3196-3233.
[Google Scholar] [CrossRef] 
[12] Shimizu, Y. (2006) M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinite Jumps. Statistical Inference for Stochastic Processes, 9, 179-225.
[Google Scholar] [CrossRef] 
[13] Shimizu, Y. and Yoshida, N. (2006) Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations. Statistical Inference for Stochastic Processes, 9, 227-277.
[Google Scholar] [CrossRef] 
[14] Hu, Y. and Long, H. (2009) Least Squares Estimator for Ornstein—Uhlenbeck Processes Driven by α-Stable Motions. Stochastic Processes and their Applications, 119, 2465-2480.
[Google Scholar] [CrossRef] 
[15] Applebaum, D. (2004) Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge.
[Google Scholar] [CrossRef] 
[16] Rosinski, J. and Woyczynski, W.A. (1986) On Itô Stochastic Integration with Respect to P-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals. Annals of Probability, 14, 271-286.
[Google Scholar] [CrossRef] 
[17] Kallenberg, O. (1992) Some Time Change Representations of Stable Integrals, via Predictable Transformations of Local Martingales. Stochastic Processes and Their Applications, 40, 199-223.
[Google Scholar] [CrossRef] 
[18] Protter, P. (2005) Stochastic Integration and Differential Equations. Vol. 21, Springer, Berlin, Heidelberg and New York.
[Google Scholar] [CrossRef] 

为你推荐