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Least squares estimation for path-distribution dependent stochastic differential equations

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  • Ren, Panpan
  • Wu, Jiang-Lun

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.

Suggested Citation

  • Ren, Panpan & Wu, Jiang-Lun, 2021. "Least squares estimation for path-distribution dependent stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005464
    DOI: 10.1016/j.amc.2021.126457
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    References listed on IDEAS

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    Cited by:

    1. Yazid Alhojilan & Hamdy M. Ahmed, 2023. "New Results Concerning Approximate Controllability of Conformable Fractional Noninstantaneous Impulsive Stochastic Evolution Equations via Poisson Jumps," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    2. Ma, Xiaocui & Yue, Haitao & Xi, Fubao, 2022. "The averaging method for doubly perturbed distribution dependent SDEs," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Ren, Panpan, 2023. "Singular McKean–Vlasov SDEs: Well-posedness, regularities and Wang’s Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 291-311.
    4. Chen, Xingyuan & dos Reis, Gonçalo, 2022. "A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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