Convergence and parameter estimation of the linear weighted-fractional self-repelling diffusion

Litan Yan, Rui Guo and Han Gao

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 7, 2390-2421

Abstract: Let Ba,b be a weighted-fractional Brownian motion with Hurst indexes a and b such that a>−1 and 0 0, ν∈R are two real parameters. The process is an analogue of the linear self-interacting diffusion (Cranston and Le Jan, Math. Ann. 303 (1995), 87-93). We introduce its large time behaviors, and the behavior presents a recursive convergence which is quite different from the asymptotic behavior of stochastic differential equations without interacting drifts. As a related question, we also consider the asymptotic behaviors of the least squares estimations of θ and ν.

Date: 2024
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DOI: 10.1080/03610926.2022.2132828

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