Related papers: Fractional Gaussian noise criterion for correlatio…
This paper aims to explore non-Markovian dynamics of nonlinear dynamical systems subjected to fractional Gaussian noise (FGN) and Gaussian white noise (GWN). A novel memory-dependent Fokker-Planck-Kolmogorov (memFPK) equation is developed…
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate…
The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic…
We propose a novel diffusion-based generative framework for financial time series that incorporates geometric Brownian motion (GBM), the foundation of the Black--Scholes theory, into the forward noising process. Unlike standard score-based…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
The price movement prediction of stock market has been a classical yet challenging problem, with the attention of both economists and computer scientists. In recent years, graph neural network has significantly improved the prediction…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations…
We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of…
We propose a data processing technique that allows searches for a stochastic background of gravitational radiation with data from a single detector. Our technique exploits the difference between the coherence time of the gravitational wave…
The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter…
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…
Based on the Heisenberg-picture analog of the master equation, we develop a method for computing the exact time dependence of noise-averaged observables for general noninteracting fermionic systems with noisy fluctuations. Upon noise…
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha…
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…
We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in…