Related papers: The Analytic Stockwell Transform and its Zeros
This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…
This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…
Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared…
The zeros of the spectrogram have proven to be a relevant feature to describe the time-frequency structure of a signal, originated by the destructive interference between components in the time-frequency plane. In this work, a…
The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to…
The analysis of non-stationary signals in non-uniformly sampled data is a challenging task. Time-integrated methods, such as the generalised Lomb-Scargle (GLS) periodogram, provide a robust statistical assessment of persistent periodicities…
This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…
The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this…
Many traditional algorithms applied in gravitational-wave astronomy rely on the assumption of Gaussian noise, a condition not always met. To meet this need, this study extends a robust statistical framework, advancing previous work on…
Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh leading to a simple approach to analyticity.…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
We consider stochastic differential equations driven by Gaussian white noise on $\R^d$. % We provide applications to models for financial %markets. Particular attention is given to the kernel $p_t,\,t\geq 0$ of the transition semigroup…
Consider an analytic Hamiltonian system near its analytic invariant torus $\mathcal T_0$ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\mathcal T_0$ is convergent and has a particular form: it is an…
In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the domain of the integral gets large (for fixed time $t$). This equation is driven by a…