Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation. (English) Zbl 1395.60042
The paper accomplishes two goals:
1) to get the asymptotic bounds with \(P=1\) for the rate of growth of the trajectories of multifunctional Brownian motion (mBm) and of some other functionals of mBm, including increments and fractional derivatives;
2) to construct consistent estimators of the unknown drift parameter in the linear and in the Ornstein-Uhlenbeck model involving mBm applying these bounds in 1).
The authors also produce asymptotic bounds with \(P=1\) for the rate of growth of the trajectories of the general Gaussian process and some functionals of it in terms of the covariance function of its increments, which generalizes previous results from Y. Kozachenko et al. [Statistics 49, No. 1, 35–62 (2015; Zbl 1396.62190)].
1) to get the asymptotic bounds with \(P=1\) for the rate of growth of the trajectories of multifunctional Brownian motion (mBm) and of some other functionals of mBm, including increments and fractional derivatives;
2) to construct consistent estimators of the unknown drift parameter in the linear and in the Ornstein-Uhlenbeck model involving mBm applying these bounds in 1).
The authors also produce asymptotic bounds with \(P=1\) for the rate of growth of the trajectories of the general Gaussian process and some functionals of it in terms of the covariance function of its increments, which generalizes previous results from Y. Kozachenko et al. [Statistics 49, No. 1, 35–62 (2015; Zbl 1396.62190)].
Reviewer: Anatoliy Swishchuk (Calgary)
MSC:
| 60G15 | Gaussian processes |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 62F10 | Point estimation |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
Gaussian process; multifunctional Brownian motion; parameter estimation; consistency; strong consistency; stochastic differentia equiationCitations:
Zbl 1396.62190References:
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