Asymptotically normal estimation of parameters of mixed fractional Brownian motion

Authors

DOI:

https://doi.org/10.17721/1812-5409.2023/2.6

Keywords:

Fractional Brownian motion, Wiener process, mixed model, parameter estimation, asymptotic distribution

Abstract

We investigate the mixed fractional Brownian motion of the form Xt = σ Wt + κ BtH, driven by a standard Brownian motion W and a fractional Brownian motion BH with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (H, κ, σ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 1/2) ∪ (1/2, 3/4).

Pages of the article in the issue: 54 - 62

Language of the article: English

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Published

2023-12-23

How to Cite

Ralchenko, K., & Yakovliev, M. (2023). Asymptotically normal estimation of parameters of mixed fractional Brownian motion. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 54–62. https://doi.org/10.17721/1812-5409.2023/2.6

Issue

Section

Algebra, Geometry and Probability Theory