Identification of the Hurst Index of a Step Fractional Brownian Motion

被引：6
|
作者：
Albert Benassi
Pierre Bertrand
Serge Cohen
Jacques Istas
机构：
[1] Université Blaise Pascal (Clermont-Ferrand II),Department IMSS BSHM
[2] Université de Versailles St Quentin,undefined
[3] Université Pierre Mendes-France,undefined
来源：
Statistical Inference for Stochastic Processes | 2000年 / 3卷 / 1-2期
关键词：
change-point detection; Hurst index; Gaussian processes; step fractional Brownian motion; semi-parametric estimation;
D O I：
10.1023/A:1009997729317
中图分类号：
学科分类号：
摘要：
We propose a semi-parametric estimator for a piece-wise constant Hurst coefficient of a step fractional Brownian motion (SFBM). For the applications, we want to detect abrupt changes of the Hurst index (which represents long-range correlation) for a Gaussian process with a.s. continuous paths. The previous model of multifractional Brownian motion give a.s. discontinuous paths at change times of the Hurst index. Thus, we first propose a new kind of Fractional Brownian Motion, the SFBM and prove some (Hölder) continuity results. After, we propose an estimator of the piecewise constant Hurst parameter and prove its consistency.
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页码：101 / 111
页数：10
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