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Acta Mathematica Scientia

, Volume 39, Issue 3, pp 691–716 | Cite as

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

  • Panpan Ren
  • Jiang-Lun WuEmail author
Article
  • 74 Downloads

Abstract

In this article, 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 this article 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-time observations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and path-distribution dependent.

Key words

McKean-Vlasov stochastic differential equation tamed Euler-Maruyama scheme weak monotonicity least squares estimator consistency asymptotic distribution 

2010 MR Subject Classification

62F12 62M05 60G52 60J75 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Computational FoundrySwansea UniversitySwanseaUK

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