Related papers: Characterization of Hida Measures in white noise a…
Supervised Gaussian denoisers exhibit limited generalization when confronted with out-of-distribution noise, due to the diverse distributional characteristics of different noise types. To bridge this gap, we propose a histogram matching…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
For a class of non-linear stochastic heat equations driven by $\alpha$-stable white noises for $\alpha\in(1,2)$ with Lipschitz coefficients, we first show the existence and pathwise uniqueness of $L^p$-valued c\`{a}dl\`{a}g solutions to…
Separating signal from noise is central to experiments. Applying well-established statistical methods effectively to LLM evals requires consideration of their unique noise characteristics. We clearly define and measure three types of noise:…
In this paper we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by…
Our main results are certain developments of the classical Poisson--Jensen formula for subharmonic functions. The basis of the classical Poisson--Jensen formula is the natural duality between harmonic measures and Green's functions. Our…
Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A…
We study an infinite dimensional analysis with respect to the measure on Schwartz space of tempered distributions, corresponding to the distributional derivative of gamma process. Laguerre polynomials being orthogonal with respect to gamma…
We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the $L^2$-distance between the spectral density operator and its best ($L^2$-)approximation by a spectral…
Algorithmic recommendation based on noisy preference measurement is prevalent in recommendation systems. This paper discusses the consequences of such recommendation on market concentration and inequality. Binary types denoting a…
The properties of precessing, coalescing binary black holes are presently inferred through comparison with two approximate models of compact binary coalescence. In this work we show these two models often disagree substantially when…
In this article, we established a large deviation principle for invariant measures of solutions of stochastic partial differential equations with two reflecting walls driven by space-time white noise.
In this paper we study the Poisson and heat equations on bounded and unbounded domains with smooth boundary with random Dirichlet boundary conditions. The main novelty of this work is a convenient framework for the analysis of such…
We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian…
Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than…
We present an orthogonal expansion for real, function-regulated, second-order random measures over $\mathbb{R}^{d}$ with measure covariance. Such a expansion, which can be seen as a Karhunen-Lo\`eve decomposition, consists in a series of…
It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities are sufficiently smooth and uniformly bounded away from zero. We show that a uniform…
It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine…
We investigate the effects of white noise on parametric resonance in $\lambda \phi^{4}$ theory. The potential $V(\phi)$ in this study is ${1/2} m^{2} \phi^{2} + {1/3} g \phi^{3} + {1/4} \lambda \phi^{4}$. An Mathieu-like equation is derived…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…