Asymptotically normal estimation of parameters of mixed fractional Brownian motion




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


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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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.



Algebra, Geometry and Probability Theory