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Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations

Panpan Ren, Jiang-lun Wu Orcid Logo

Acta Mathematica Scientia, Volume: 39, Issue: 3, Pages: 691 - 716

Swansea University Authors: Panpan Ren, Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1007/s10473-019-0305-4

Abstract

In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establish...

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Published in: Acta Mathematica Scientia
ISSN: 0252-9602 1572-9087
Published: Springer Science and Business Media LLC 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa44860
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Abstract: In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of our paper lie in three aspects: (i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-timeobservations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (e.g., H\"older continuous) and path-distribution dependent.
Keywords: McKean-Vlasov stochastic differential equation, tamed Euler-Maruyama scheme, weak monotonicity, least squares estimator, consistency, asymptotic distribution.
College: Faculty of Science and Engineering
Funders: None
Issue: 3
Start Page: 691
End Page: 716

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