Least squares estimation for path-distribution dependent stochastic differential equations

Panpan Ren; Jiang-Lun Wu

doi:10.1016/j.amc.2021.126457

Least squares estimation for path-distribution dependent stochastic differential equations

Panpan Ren, Jiang-Lun Wu^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

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 ε>0. The estimator, based on n (where n ∈ N) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as ε → 0 and n → ∞. 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.

© 2021 Elsevier Inc. All rights reserved.

Original language	English
Article number	126457
Journal	Applied Mathematics and Computation
Volume	410
Online published	29 Jun 2021
DOIs	https://doi.org/10.1016/j.amc.2021.126457
Publication status	Published - 1 Dec 2021
Externally published	Yes

Research Keywords

Asymptotic distribution
Consistency
Least squares estimator
Path-distribution dependent stochastic differential equation

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10.1016/j.amc.2021.126457

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title = "Least squares estimation for path-distribution dependent stochastic differential equations",

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 ε>0. The estimator, based on n (where n ∈ N) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as ε → 0 and n → ∞. 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.{\textcopyright} 2021 Elsevier Inc. All rights reserved. ",

keywords = "Asymptotic distribution, Consistency, Least squares estimator, Path-distribution dependent stochastic differential equation",

author = "Panpan Ren and Jiang-Lun Wu",

year = "2021",

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doi = "10.1016/j.amc.2021.126457",

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TY - JOUR

T1 - Least squares estimation for path-distribution dependent stochastic differential equations

AU - Ren, Panpan

AU - Wu, Jiang-Lun

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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 ε>0. The estimator, based on n (where n ∈ N) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as ε → 0 and n → ∞. 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.© 2021 Elsevier Inc. All rights reserved.

AB - 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 ε>0. The estimator, based on n (where n ∈ N) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as ε → 0 and n → ∞. 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.© 2021 Elsevier Inc. All rights reserved.

KW - Asymptotic distribution

KW - Consistency

KW - Least squares estimator

KW - Path-distribution dependent stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=85108877466&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85108877466&origin=recordpage

U2 - 10.1016/j.amc.2021.126457

DO - 10.1016/j.amc.2021.126457

M3 - RGC 21 - Publication in refereed journal

SN - 0096-3003

VL - 410

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 126457

ER -

Least squares estimation for path-distribution dependent stochastic differential equations

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Research Keywords

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