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

Autor:	Dozzi, Marco, Kozachenko, Yuriy, Mishura, Yuliya, Ralchenko, Kostiantyn
Rok vydání:	2016
Předmět:	Mathematics - Probability 60G15 60G22 62F10 62F12
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.05848 Zobrazit plný text záznamu View this record from Arxiv