Related papers: Limit theorems for stationary increments L\'evy dr…
In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while…
In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…
In this paper we obtain new limit theorems for variational functionals of high frequency observations of stationary increments L\'evy driven moving averages. We will see that the asymptotic behaviour of such functionals heavily depends on…
In this paper we present some new limit theorems for power variations of stationary increment L\'{e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528,…
In this article we consider L\'evy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
We study a random walk on a point process given by an ordered array of points $(\omega_k, \, k \in \mathbb{Z})$ on the real line. The distances $\omega_{k+1} - \omega_k$ are i.i.d. random variables in the domain of attraction of a…
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
We study long time behavior of integrated trawl processes introduced by Barndorff-Nielsen. The trawl processes form a class of stationary infinitely divisible processes, described by an infinitely divisible random measure (L\'evy base) and…
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…
In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $\beta$-stable L\'evy processes, $\beta \in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of…
We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…