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On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations

Jingjie Li, Jiang-lun Wu Orcid Logo

Advances in Difference Equations, Volume: 2016, Issue: 1

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1186/s13662-016-0819-1

Abstract

We study the parameter estimation for mean-reversion type stochastic differential equations driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at discrete (regularly spaced) time instants. The least square method is utilized to derive an asymptotically con...

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Published in: Advances in Difference Equations
ISSN: 1687-1847
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28504
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first_indexed 2016-06-02T18:23:43Z
last_indexed 2018-02-09T05:12:42Z
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spelling 2017-02-22T11:11:32.0141978 v2 28504 2016-06-02 On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2016-06-02 SMA We study the parameter estimation for mean-reversion type stochastic differential equations driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at discrete (regularly spaced) time instants. The least square method is utilized to derive an asymptotically consistent estimator. Discussions on the rate of convergence of the least square estimator are presented. The new feature of this study is that, due to the mean-reversion type drift coefficient in the stochastic differential equations, we have to use the Girsanov transformation to simplify the equations, which then gives rise to the corresponding convergence of the least square estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure. Journal Article Advances in Difference Equations 2016 1 1687-1847 mean-reversiontypeSDEs;Girsanovtransformation;leastsquare estimator (LSE); discrete observation; consistency of least square estimator; asymptotic distribution of LSE 31 12 2016 2016-12-31 10.1186/s13662-016-0819-1 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2017-02-22T11:11:32.0141978 2016-06-02T17:12:30.4546819 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jingjie Li 1 Jiang-lun Wu 0000-0003-4568-7013 2 0028504-22022017111124.pdf AdvancesDiffEqLiWu.pdf 2017-02-22T11:11:24.7130000 Output 1636363 application/pdf Accepted Manuscript true 2017-02-22T00:00:00.0000000 false eng
title On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
spellingShingle On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
Jiang-lun Wu
title_short On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
title_full On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
title_fullStr On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
title_full_unstemmed On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
title_sort On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Jingjie Li
Jiang-lun Wu
format Journal article
container_title Advances in Difference Equations
container_volume 2016
container_issue 1
publishDate 2016
institution Swansea University
issn 1687-1847
doi_str_mv 10.1186/s13662-016-0819-1
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We study the parameter estimation for mean-reversion type stochastic differential equations driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at discrete (regularly spaced) time instants. The least square method is utilized to derive an asymptotically consistent estimator. Discussions on the rate of convergence of the least square estimator are presented. The new feature of this study is that, due to the mean-reversion type drift coefficient in the stochastic differential equations, we have to use the Girsanov transformation to simplify the equations, which then gives rise to the corresponding convergence of the least square estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure.
published_date 2016-12-31T03:34:41Z
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score 11.013148

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