32 citations · 35 across the 10 of their papers we have counts for
10 papers
CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index
Kestutis Kubilius
We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on . Though the approach we use is well kno…
A short note on a class of statistics for estimation of the Hurst index of fractional Brownian motion
Kestutis Kubilius, Viktor Skorniakov
We propose some class of statistics suitable for estimation of the Hurst index of the fractional Brownian motion based on the second order increments of an observed discrete trajec…
On comparison of the estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process
Kestutis Kubilius, Dmitrij Melichov
We study some estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process and prove that they are strongly consistent and most of them…
On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion
Kestutis Kubilius, Viktor Skorniakov
Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete…
Exact confidence intervals of the extended Orey index for Gaussian processes
Kestutis Kubilius, Dmitrij Melichov
In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observatio…
Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index
Kestutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko +1
We consider Langevin equation involving fractional Brownian motion with Hurst index . Its solution is the fractional Ornstein-Uhlenbeck process and with unknown dr…
Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift
Kestutis Kubilius, Viktor Skorniakov, Dmitrij Melichov
Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are pr…
On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion
K. Kubilius, V. Skorniakov, D. Melichov
Strongly consistent and asymptotic normal estimators of the Hurst index of a stochastic differential equation driven by a fractional Brownian motion are proposed. The estimators ar…
On estimation of the Orey index for a class of Gaussian processes
Kestutis Kubilius
Orey suggested the definition of some index for Gaussian processes with stationary increments which determines various properties of the sample paths of this process. We give an ex…
The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation
K. Kubilius, Y. Mishura
We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according…