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Nonparametric estimation for distribution dependent SDEs driven by fractional brownian motions with random effects

Author

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  • Guangjun Shen

    (Anhui Normal University)

  • Qian Yu

    (Nanjing University of Aeronautics and Astronautics)

  • Huan Zhou

    (Anhui Normal University)

Abstract

In this paper, we study a nonparametric estimation of random effects from the following distribution dependent SDE driven by fractional Brownian motions $$\begin{aligned} dX^j_t=\beta _jb(t,X^j_t,\mathcal {L}_{X_t^j})dt+\varepsilon \sigma (t, \mathcal {L}_{X^j_t})dB_t^{j,H}, ~X^j_0=x^j_0, ~0\le t\le T, \end{aligned}$$ where $$j=1,2,\cdots,N$$ , $$\mathcal {L}_{X^j_t}$$ denotes the law of $$X^j_t$$ , $$B_t^{1, H},\cdots,B_t^{N, H}$$ are independent fractional Brownian motions with common Hurst parameter $$H\in (1/2,1)$$ and $$\beta _j$$ is random variable independent of $$B^{j,H}$$ . This result extends the existing results of non parametric estimation to the case of distribution dependent. Moreover, we consider the estimation for the density function of $$\beta _j$$ under weaker conditions of kernel function and study the corresponding asymptotic distribution.

Suggested Citation

  • Guangjun Shen & Qian Yu & Huan Zhou, 2025. "Nonparametric estimation for distribution dependent SDEs driven by fractional brownian motions with random effects," Statistical Papers, Springer, vol. 66(5), pages 1-22, August.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01742-6
    DOI: 10.1007/s00362-025-01742-6
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    1. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
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    3. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic Theory For Estimating Drift Parameters In The Fractional Vasicek Model," Econometric Theory, Cambridge University Press, vol. 35(1), pages 198-231, February.
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    5. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
    6. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
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