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Modern Stochastics: Theory and Applications


Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations
Volume 11, Issue 1 (2024), pp. 1–29
Pub. online: 5 December 2023      Type: Research Article      Open accessOpen Access
Received
3 August 2023
Revised
2 November 2023
Accepted
2 November 2023
Published
5 December 2023

Abstract

The object of investigation is the mixed fractional Brownian motion of the form ${X_{t}}=\kappa {B_{t}^{{H_{1}}}}+\sigma {B_{t}^{{H_{2}}}}$, driven by two independent fractional Brownian motions ${B_{1}^{H}}$ and ${B_{2}^{H}}$ with Hurst parameters ${H_{1}}\lt {H_{2}}$. Strongly consistent estimators of unknown model parameters ${({H_{1}},{H_{2}},{\kappa ^{2}},{\sigma ^{2}})^{\top }}$ are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for $0\lt {H_{1}}\lt {H_{2}}\lt \frac{3}{4}$.

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© 2024 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Fractional Brownian motion mixed model strong consistency ergodic theorem asymptotic normality

MSC2010
60G22 62F10 62F12

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