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We study the asymptotic behaviour of sequences of integral functionals depending on moving anisotropies. We introduce and describe the relevant functional setting, establishing uniform Meyers-Serrin type approximations, Poincar\'e…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
We construct absolute continuous stochastic processes that converge to anisotropic fractional and multifractional Brownian sheets in Besov-type spaces.
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of…
We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…
Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi-Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in…
In this paper we study propagation of the high frequency electromagnetic waves in a curved spacetime. We discuss a so call spinoptics approach which generalizes a well known geometric optics approximation and allows one to take into account…
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
The problem of optimal linear estimation of functionals depending on the unknown values of a random field $\zeta(t,x)$, which is mean-square continuous periodically correlated with respect to time argument $t\in\mathbb R$ and isotropic on…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give…
Surgical scene segmentation is crucial for robot-assisted laparoscopic surgery understanding. Current approaches face two challenges: (i) static image limitations including ambiguous local feature similarities and fine-grained structural…
We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference…
Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…