Related papers: The Analytic Stockwell Transform and its Zeros
This thesis is concerned with the behavior of random analytic functions. In particular, we are interested in the value distribution of Taylor series with independent random coefficients. We begin with a study of the properties of Fourier…
We study the asymptotic behaviour of the solutions of a functional- differential equation with rescaling, the so-called pantograph equation. From this we derive asymptotic information about the zeros of these solutions.
This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-posedness of the posterior measure are studied. The abstract…
In this article, we give a new proof of the It\^o formula for some integral processes related to the space-time L\'evy white noise introduced in Balan (2015) as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two…
A gravitational-wave background can be detected in pulsar-timing-array data as Hellings--Downs correlations among the timing residuals measured for different pulsars. The optimal statistic implements this concept as a classical…
Stochastic resonance is a phenomenon where a noise of appropriate intensity enhances the input signal strength. In this work, by employing the recently developed convex optimization methods in the context of dynamical systems and stochastic…
This paper reports on recent results related to audiophonic signals encoding using time-scale and time-frequency transform. More precisely, non-linear, structured approximations for tonal and transient components using local cosine and…
Following Wiener, we consider the zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We show that the variance of the number of zeroes in a long horizontal rectangle $[0,T]\times…
I present a method for lossy transform coding of digital audio that uses the Weyl symbol calculus for constructing the encoding and decoding transformation. The method establishes a direct connection between a time-frequency representation…
In this paper, we study the convolution structure in the special affine Fourier transform domain to combine the advantages of the well known special affine Fourier and Stockwell transforms into a novel integral transform coined as special…
We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise. The main ingredient of our method depends on the…
In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a…
Classical Gaussian white noise in communications and signal processing is viewed as the limit of zero mean second order Gaussian processes with a compactly supported flat spectral density as the support goes to infinity. The difficulty of…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…