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

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  • Litan Yan
  • Rui Guo
  • Han Gao

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.

Suggested Citation

  • Litan Yan & Rui Guo & Han Gao, 2024. "Convergence and parameter estimation of the linear weighted-fractional self-repelling diffusion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(7), pages 2390-2421, April.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:7:p:2390-2421
    DOI: 10.1080/03610926.2022.2132828
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