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

Leyi Shen, Xiaoyu Xia and Litan Yan

Statistics & Probability Letters, 2022, vol. 181, issue C

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.

Keywords: α-stable motion; Self-interacting diffusion; Least squares estimation; Asymptotic distribution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109259

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