Least squares estimation for \(\alpha\)-fractional bridge with discrete observations
type: Item
instance of: scholarly article
title: Least squares estimation for \(\alpha\)-fractional bridge with discrete observations
zbMATH Open document ID: 1474.62302
DOI: 10.1155/2014/748376
author: Xiuwei Yin
author: Guangjun Shen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider a fractional bridge defined as \(d X_t = - \alpha (X_t /(T - t)) d t + d B_t^H\), \(0 \leq t < T\), where \(B^H\) is a fractional Brownian motion of Hurst parameter \(H > 1 / 2\) and parameter \(\alpha > 0\) is unknown. We are interested in the problem of estimating the unknown parameter \(\alpha > 0\). Assume that the process is observed at discrete time \(t_i = i \Delta_n, i = 0, \ldots, n\), and \(T_n = n \Delta_n\) denotes the length of the ``observation window.'' We construct a least squares estimator \(\widehat{\alpha}_n\) of \(\alpha\) which is consistent; namely, \(\widehat{\alpha}_n\) converges to \(\alpha\) in probability as \(n \rightarrow \infty\).
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 60G22
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 62M05
zbMATH DE Number: 7023012
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/748376
OpenAlex ID: W2032657658
Wikidata QID: Q59041208
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description: scientific article; zbMATH DE number 7023012