Identification of a Locally Self-similar Gaussian Process by Using Convex Rearrangements

被引：2
作者：
A. Philippe
E. Thilly
机构：
[1] U.F.R de Mathématiques Bât. M2,Laboratoire de mathématiques appliquées
[2] Université de Lille I,Laboratoire de mathématiques SDAD
[3] Université de Caen—Bât. S3,undefined
来源：
Methodology And Computing In Applied Probability | 2002年 / 4卷 / 2期
关键词：
convex rearrangements; fractal dimension; Gaussian process; Hölder index; self-similar process;
D O I：
10.1023/A:1020645709273
中图分类号：
学科分类号：
摘要：
We propose a new approach for identifying a locally self-similar Gaussian process. The method is based on the asymptotic behavior of convex rearrangement obtained by Davydov and Thilly (2002). Some simulations illustrate the behavior of the resulting estimates in the particular case of the fractional Brownian motion.
引用
收藏
页码：195 / 209
页数：14
相关论文
共 12 条
[1]  
Davydov Y.(2002)Convex rearrangements of stable processes J. of Math. Sciences 92 4010-4016
[2]  
Feuergever A.(1994)Estimation of fractal index and fractal dimension of Gaussian process by counting the number of level crossings Journal of Times Series Analysis 15 587-606
[3]  
Hall P.(1994)On the relationship between fractal dimension and fractal index for stationary stochastic processes Annals of Probability 4 241-253
[4]  
Wood A. T. A.(1997)Quadratic variations and estimation of the local Hölder index of Gaussian process Ann. Inst. Henri Poincaré 33 407-436
[5]  
Hall P.(1997)Estimating the fractal dimension of a locally self-similar Gaussian process by using increments Journal of the Royal Statistic Society B 59 679-699
[6]  
Roy R.(1994)Simulation of stationary Gaussian processes in [0, 1] J. Comput. Graph. Stat 3 409-432
[7]  
Istas J.(undefined)undefined undefined undefined undefined-undefined
[8]  
Lang G.(undefined)undefined undefined undefined undefined-undefined
[9]  
Kent J. T.(undefined)undefined undefined undefined undefined-undefined
[10]  
Wood A. T. A.(undefined)undefined undefined undefined undefined-undefined
12