Related papers: Functional spaces and operators connected with som…
We characterize the local smoothness and the asymptotic growth rate of the L\'evy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is…
We survey different approaches to study the invariance of the white noise for the periodic KdV. We mainly discuss the following two methods. First, we discuss the PDE method, following Bourgain \cite{BO4}, in a general framework. Then, we…
Using key tools such as It\^o formula for general semi-martingales, moments estimates for L\'{e}vy-type stochastic integrals and properties of regular varying functions we find conditions under which solutions of stochastic differential…
We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the…
Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…
In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…
We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization…
We experimentally investigate the quantum-noise performance of a conventional heterodyne detector and find significant discrepancy between experiment and theory. Further investigations are highly recommended for deeper insight into the…
In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
We study natural invariance properties of functionals defined on L\'evy processes and show that they can be described by a simplified structure of the deterministic chaos kernels in It\^o's chaos expansion. These structural properties of…
The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and…
Non-equilibrium noise is characterized as noise realizations where external agitations disrupt the harmonic equilibrium of Brownian motion. Excitations in a particle's random walk into a so-called L\'evy flight changes the distribution of…
We consider a L\'evy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…
In this article, we introduce a L\'evy analogue of the spatially homogeneous Gaussian noise of Dalang (1999), and we construct a stochastic integral with respect to this noise. The spatial covariance of the noise is given by a tempered…