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Least squares estimation for path-distribution dependent stochastic differential equations
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...
| Published in: | Applied Mathematics and Computation |
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| ISSN: | 0096-3003 0096-3003 |
| Published: |
Elsevier BV
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa57110 |
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| 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 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. |
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| Keywords: |
Path-distribution dependent stochastic differential equation, least squares estimator, consistency, asymptotic distribution. |
| College: |
Faculty of Science and Engineering |
| Start Page: |
126457 |