Related papers: A note on Herglotz's theorem for time series on fu…
We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general…
In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
A statistical hypothesis test for long range dependence (LRD) is formulated in the spectral domain for functional time series in manifolds. The elements of the spectral density operator family are assumed to be invariant with respect to the…
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…
We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular…
The article is devoted to a new proof of the expansion for iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process. The above expansion is based on Hermite polynomials and generalized multiple…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…
We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The…
We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
We prove the following extension of the Wiener--Wintner Theorem in Ergodic Theor and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows $ (X,\mu , T_t)$ and $ f\in L^p (X,\mu)$, there is a set…
In this note we define and study a Hilbert space-valued stochastic integral of operator-valued functions with respect to Hilbert space-valued measures. We show that this integral generalizes the classical Ito stochastic integral of adapted…
In this paper we give a new proof to an Engelbert-Schmidt type zero-one law for time-homogeneous diffusions, which provides deterministic criteria for the convergence of integral functional of diffusions. Our proof is based on a slightly…
We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…