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Least squares estimation for the linear self-repelling diffusion driven by α-stable motions

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  • Shen, Leyi
  • Xia, Xiaoyu
  • Yan, Litan

Abstract

In this paper, we consider parameter estimations of the linear self-repelling diffusion Xtα=Mtα−θ∫0t∫0s(Xsα−Xrα)drds+νt, where θ<0, ν∈R and Mα is a symmetrical α-stable motion on R (1<α<2). The process is an analogue of the self-repelling diffusion (see Durrett and Rogers (1992) and Cranston and Le Jan (1995)). By using least squares method, we study estimators of θ and ν and give their asymptotic distributions under the discrete observation.

Suggested Citation

  • Shen, Leyi & Xia, Xiaoyu & Yan, Litan, 2022. "Least squares estimation for the linear self-repelling diffusion driven by α-stable motions," Statistics & Probability Letters, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002212
    DOI: 10.1016/j.spl.2021.109259
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    1. Iacus, Stefano Maria & Uchida, Masayuki & Yoshida, Nakahiro, 2009. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1580-1600, May.
    2. Herrmann, Samuel & Scheutzow, Michael, 2004. "Rate of convergence of some self-attracting diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 41-55, May.
    3. Li, Zenghu & Ma, Chunhua, 2015. "Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3196-3233.
    4. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
    5. Hu, Yaozhong & Long, Hongwei, 2009. "Least squares estimator for Ornstein-Uhlenbeck processes driven by [alpha]-stable motions," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2465-2480, August.
    6. Kallenberg, Olav, 1992. "Some time change representations of stable integrals, via predictable transformations of local martingales," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 199-223, March.
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