相关论文: Probability Density Function of Kerr Effect Phase …
Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern…
According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
We propose a method for quantum noise extraction from the interference of laser pulses with random phase. Our technique is based on the calculation of a parameter, which we called the quantum reduction factor, and which allows determining…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We consider a model for 2D electrons in a very strong magnetic field (i.e. projected onto a single Landau level) and a random potential $V$. The computation of the averaged Green function for this system reduces to calculating the averaged…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
Auto- and cross-spectral density functions for dynamic {random} fields and power are derived. These are based on first- and second-order Pad\'{e} approximants of correlation functions expanded in terms of spectral moments. The second-order…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
The Gaussian mixture distribution is important in various statistical problems. In particular it is used in the Gaussian-sum filter and smoother for linear state-space model with non-Gaussian noise inputs. However, for this method to be…
We present a statistical analysis of a variant of the periodogram method that forms power spectral density estimates by cross-correlating the discrete Fourier transforms of adjacent time windows. The proposed estimator is closely related to…
The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data…
I calculate the statistics of correlation of two digitized noiselike signals, which are drawn from complex Gaussian distributions, sampled, quantized, correlated, and averaged. Averaged over many such samples, the correlation r approaches a…
This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The contributions of the paper consists both in the derivation…
In estimation theory, the Kushner equation provides the evolution of the probability density of the state of a dynamical system given continuous-time observations. Building upon our recent work, we propose a new way to approximate the…
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
We present a continuous-time probabilistic approach for estimating the chirp signal and its instantaneous frequency function when the true forms of these functions are not accessible. Our model represents these functions by non-linearly…
The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…