Least squares estimation for path-distribution dependent stochastic differential equations

Ren, Panpan; Wu, Jiang-lun

doi:10.1016/j.amc.2021.126457

Journal article 874 views 131 downloads

Least squares estimation for path-distribution dependent stochastic differential equations

Panpan Ren, Jiang-lun Wu

Applied Mathematics and Computation, Volume: 410, Start page: 126457

Swansea University Authors: Panpan Ren, Jiang-lun Wu

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DOI (Published version): 10.1016/j.amc.2021.126457

Abstract

We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter $\epsilon>0$. The estimator, based on $n$ (where $n\in\mathbb{N}$) discrete time observations of the stoch...

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Published in:	Applied Mathematics and Computation
ISSN:	0096-3003 0096-3003
Published:	Elsevier BV 2021
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa57110
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first_indexed	2021-06-12T13:20:29Z
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spelling	2022-08-21T21:25:13.1280371 v2 57110 2021-06-12 Least squares estimation for path-distribution dependent stochastic differential equations 730d4aa09026fef7d3d03653815692aa Panpan Ren Panpan Ren true false dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2021-06-12 We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter $\epsilon>0$. The estimator, based on $n$ (where $n\in\mathbb{N}$) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as $\epsilon \to 0$ and $n \to \infty$. This indicates that the least squares estimator obtained is consistent with the true value. Moreover, we obtain the rate of convergence and derive the asymptotic distribution of least squares estimator. Journal Article Applied Mathematics and Computation 410 126457 Elsevier BV 0096-3003 0096-3003 Path-distribution dependent stochastic differential equation, least squares estimator, consistency, asymptotic distribution. 1 12 2021 2021-12-01 10.1016/j.amc.2021.126457 http://dx.doi.org/10.1016/j.amc.2021.126457 COLLEGE NANME COLLEGE CODE Swansea University Other 2022-08-21T21:25:13.1280371 2021-06-12T14:04:37.3055116 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Panpan Ren 1 Jiang-lun Wu 0000-0003-4568-7013 2 57110__20142__eca0bd774ed54620b1ed03a484671b09.pdf RenWu.pdf 2021-06-12T14:16:35.8467885 Output 2290785 application/pdf Accepted Manuscript true 2022-06-29T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title	Least squares estimation for path-distribution dependent stochastic differential equations
spellingShingle	Least squares estimation for path-distribution dependent stochastic differential equations Panpan Ren Jiang-lun Wu
title_short	Least squares estimation for path-distribution dependent stochastic differential equations
title_full	Least squares estimation for path-distribution dependent stochastic differential equations
title_fullStr	Least squares estimation for path-distribution dependent stochastic differential equations
title_full_unstemmed	Least squares estimation for path-distribution dependent stochastic differential equations
title_sort	Least squares estimation for path-distribution dependent stochastic differential equations
author_id_str_mv	730d4aa09026fef7d3d03653815692aa dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv	730d4aa09026fef7d3d03653815692aa_*_Panpan Ren dbd67e30d59b0f32592b15b5705af885_*_Jiang-lun Wu
author	Panpan Ren Jiang-lun Wu
author2	Panpan Ren Jiang-lun Wu
format	Journal article
container_title	Applied Mathematics and Computation
container_volume	410
container_start_page	126457
publishDate	2021
institution	Swansea University
issn	0096-3003 0096-3003
doi_str_mv	10.1016/j.amc.2021.126457
publisher	Elsevier BV
college_str	Faculty of Science and Engineering
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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
url	http://dx.doi.org/10.1016/j.amc.2021.126457
document_store_str	1
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description	We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter $\epsilon>0$. The estimator, based on $n$ (where $n\in\mathbb{N}$) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as $\epsilon \to 0$ and $n \to \infty$. This indicates that the least squares estimator obtained is consistent with the true value. Moreover, we obtain the rate of convergence and derive the asymptotic distribution of least squares estimator.
published_date	2021-12-01T04:12:36Z
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score	11.037144

Least squares estimation for path-distribution dependent stochastic differential equations

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