Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation

Marco Dozzi (), Yuriy Kozachenko (), Yuliya Mishura () and Kostiantyn Ralchenko ()
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Marco Dozzi: Université de Lorraine
Yuriy Kozachenko: Taras Shevchenko National University of Kyiv
Yuliya Mishura: Taras Shevchenko National University of Kyiv
Kostiantyn Ralchenko: Taras Shevchenko National University of Kyiv

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 1, No 2, 52 pages

Abstract: Abstract We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein–Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of multifractional Brownian motion (mBm) and of some other functionals of mBm, including increments and fractional derivatives. As the auxiliary results having independent interest, we produce the asymptotic bounds with probability 1 for the rate of the growth of the trajectories of the general Gaussian process and some functionals of it, in terms of the covariance function of its increments.

Keywords: Gaussian process; Multifractional Brownian motion; Parameter estimation; Consistency; Strong consistency; Stochastic differential equation; 60G15; 60G22; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11203-016-9147-z

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