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

Guangjun Shen (), Qian Yu () and Huan Zhou ()
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Guangjun Shen: Anhui Normal University
Qian Yu: Nanjing University of Aeronautics and Astronautics
Huan Zhou: Anhui Normal University

Statistical Papers, 2025, vol. 66, issue 5, No 21, 22 pages

Abstract: 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.

Keywords: Density estimator; Distribution dependent SDE; Fractional Brownian motion; Random effects (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01742-6

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