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Kestutis Kubilius

Publications and source records attributed to Kestutis Kubilius.

8 recordsLinked to original sources
arXiv2020

CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index

We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on $[0,T]$. Though the approach we use is well known in the literature, the conditions under which the CLT holds are usually based on differentiability of the corresponding covariance function. In our case, we replace differentiability conditions by the convergence of the scaled sums of the second-order moments. To illustrate the usefulness and easiness of use of the approach, we apply the obtained CLT to proving the asymptotic normality of the estimator of the Orey index of a subfractional Brownian motion.

math.PR↗
arXiv2015

Exact confidence intervals of the extended Orey index for Gaussian processes

In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observations of the underlying process. The obtained result is applied to Gaussian processes with the Orey index which not necessarily have stationary increments.

math.PR↗
arXiv2015

On estimation of the Orey index for a class of Gaussian processes

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 extension of the definition of the Orey index for a second order stochastic processes which may not have stationary increments and estimate the Orey index for Gaussian process from discrete observations of its sample paths.

math.PR↗
arXiv2015

Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index $H\in(0,\frac12)$

We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $θ$. We construct the estimator that is similar in form to maximum likelihood estimator for Langevin equation with standard Brownian motion. Observations are discrete in time. It is assumed that the interval between observations is $n^{-1}$, i.e. tends to zero (high frequency data) and the number of observations increases to infinity as $n^m$ with $m>1$. It is proved that for positive $θ$ the estimator is strongly consistent for any $m>1$ and for negative $θ$ it is consistent when $m>\frac{1}{2H}$.

math.PR↗