Small-time behaviour of Lévy processes.
Some remarks on duality of stationary sequences
The paper clarifies the connection between Urbanik's and Miamee and Pourahmadi's concepts of duality for univariate weakly stationary random sequences. Some of Urbanik's results are proved in an alternative way and at the same time generalized to the multivariate case.
Spectral decomposition of locally stationary random processes
Spectral dilation of operator-valued measures and its application to infinite-dimensional harmonizable processes
Spectrum decomposition for stationary weakly isotropic random fields with bounded range interactions
Spectrum of randomly sampled multivariate ARMA models
The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.
Stationäre zufällige Punktfolgen. I.
Stationäre zufällige Punktfolgen. III.
Stationary distribution of absolute autoregression
A procedure for computation of stationary density of the absolute autoregression (AAR) model driven by white noise with symmetrical density is described. This method is used for deriving explicit formulas for stationary distribution and further characteristics of AAR models with given distribution of white noise. The cases of Gaussian, Cauchy, Laplace and discrete rectangular distribution are investigated in detail.
Stationary distribution of some nonlinear processes
Stationary excursions
Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres
We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.
Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres∗∗∗
We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.
Statistical properties of long return times in type I intermittency.
Strong law of large numbers under a general moment condition.
Subordination of infinite-dimensional stationary stochastic processes
Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions
Let be a stochastically continuous, separable, Gaussian process with . A sufficient condition, in terms of the monotone rearrangement of , is obtained for to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.
Sungularity as -regularity and vice versa
Superposition of diffusions with linear generator and its multifractal limit process
In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...
Superposition of Diffusions with Linear Generator and its Multifractal Limit Process
In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...