Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process

We study the minimum Skorohod distance estimation [Formula: see text] and minimum [Formula: see text] -norm estimation [Formula: see text] of the drift parameter θ of a stochastic differential equation [Formula: see text] , [Formula: see text] , where [Formula: see text] is a fractional Lévy process...

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Detalles Bibliográficos
Autores principales: Shen, Guangjun, Li, Yunmeng, Gao, Zhenlong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6311196/
https://www.ncbi.nlm.nih.gov/pubmed/30839924
http://dx.doi.org/10.1186/s13660-018-1951-0
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author Shen, Guangjun
Li, Yunmeng
Gao, Zhenlong
author_facet Shen, Guangjun
Li, Yunmeng
Gao, Zhenlong
author_sort Shen, Guangjun
collection PubMed
description We study the minimum Skorohod distance estimation [Formula: see text] and minimum [Formula: see text] -norm estimation [Formula: see text] of the drift parameter θ of a stochastic differential equation [Formula: see text] , [Formula: see text] , where [Formula: see text] is a fractional Lévy process, [Formula: see text] . We obtain their consistency and limit distribution for fixed T, when [Formula: see text] . Moreover, we also study the asymptotic laws of their limit distributions for [Formula: see text] .
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spelling pubmed-63111962019-01-10 Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process Shen, Guangjun Li, Yunmeng Gao, Zhenlong J Inequal Appl Research We study the minimum Skorohod distance estimation [Formula: see text] and minimum [Formula: see text] -norm estimation [Formula: see text] of the drift parameter θ of a stochastic differential equation [Formula: see text] , [Formula: see text] , where [Formula: see text] is a fractional Lévy process, [Formula: see text] . We obtain their consistency and limit distribution for fixed T, when [Formula: see text] . Moreover, we also study the asymptotic laws of their limit distributions for [Formula: see text] . Springer International Publishing 2018-12-29 2018 /pmc/articles/PMC6311196/ /pubmed/30839924 http://dx.doi.org/10.1186/s13660-018-1951-0 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Shen, Guangjun
Li, Yunmeng
Gao, Zhenlong
Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title_full Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title_fullStr Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title_full_unstemmed Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title_short Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process
title_sort parameter estimation for ornstein–uhlenbeck processes driven by fractional lévy process
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6311196/
https://www.ncbi.nlm.nih.gov/pubmed/30839924
http://dx.doi.org/10.1186/s13660-018-1951-0
work_keys_str_mv AT shenguangjun parameterestimationforornsteinuhlenbeckprocessesdrivenbyfractionallevyprocess
AT liyunmeng parameterestimationforornsteinuhlenbeckprocessesdrivenbyfractionallevyprocess
AT gaozhenlong parameterestimationforornsteinuhlenbeckprocessesdrivenbyfractionallevyprocess

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