Related papers: Characterization of Hida Measures in white noise a…
The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white…
This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method…
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure $\mu$. We show that the average of regular enough test functions with respect to…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…
This paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to non-Gaussian white noise calculus, see \cite{KSS96}. We use a known unitary isomorphism between Poisson and compound Poisson spaces…
Homodyne tomography provides a way for measuring generic field-operators. Here we analyze the determination of the most relevant quantities: intensity, field, amplitude and phase. We show that tomographic measurements are affected by…
It is possible to construct L\'evy white noises as generalized random processes in the sense of Gel'fand and Vilenkin, or as an independently scattered random measures introduced by Rajput and Rosinski. In this article, we unify those two…
In this article indicators to describe the "beauty" of noises are proposed. Rhythmic, tonal and harmonic suavity are introduced. They give a characterization of a noise in terms of rhythmic regularity (rhythmic suavity), of auditory…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
The purpose of these lectures is threefold: We first give a short survey of the Hida white noise calculus, and in this context we introduce the Hida-Malliavin derivative as a stochastic gradient with values in the Hida stochastic…
High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence…
We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…
We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and…
Feature selection has remained a daunting challenge in machine learning and artificial intelligence, where increasingly complex, high-dimensional datasets demand principled strategies for isolating the most informative predictors. Despite…
Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several…
It is natural to ask whether "positivity" of white noise operators can be discussed in some sense and characterized. To answer this question, we consider the Gel'fand triple over the Complex Gaussian space $(\ce'_c,\m_c)$, i.e.…
In this paper, we focus on the following testing problem: assume that we are given observations of a real-valued signal along the grid $0,1,\ldots,N-1$, corrupted by white Gaussian noise. We want to distinguish between two hypotheses: (a)…