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An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild...
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High Excursions of a Quadratic form for a Gaussian Stationary Vector Process
Exact asymptotic behavior is given for high excursion probabilities of a quadratic form for a zero-mean Gaussian stationary vector process with...
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An informatic approach to a long memory stationary process
Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data. Most of the definitions concerning the...
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Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence
AbstractThe paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity...
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Estimation of a Function in a Gaussian Stationary Noise
Upper bounds are constructed for minimax risk in the problem of estimating the unknown pseudoperiodic vector function observed against the background...
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Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data
We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement...
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A Lower Bound for Minimax Risk in a Problem of Estimating a Function in Stationary Gaussian Noise
A lower bound for minimax risk is constructed for the problem of estimating an unknown pseudoperiodic function observed in Gaussian stationary noise...
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An Approximate Algorithm for Simulating Stationary Discrete Random Processes with Bivariate Distributions of Their Consecutive Components in the Form of Mixtures of Gaussian Distributions
AbstractThe paper presents an approximate algorithm for modeling a stationary discrete random process with marginal and bivariate distributions of...
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Class GP: Gaussian Process Modeling for Heterogeneous Functions
Gaussian Processes (GP) are a powerful framework for modeling expensive black-box functions and have thus been adopted for various challenging...
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Gaussian process hydrodynamics
We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and...
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On the Shape of a High Excursion of a Gaussian Stationary Process
We investigate the shape of an excursion above a high level u by a stationary Gaussian process. The shape depends on the conditioned mean and...
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Improving the Lag Window Estimators of the Spectrum and Memory for Long-Memory Stationary Gaussian Processes
Gaussian process (GP) is a stochastic process that has been successfully applied in finance, black-box modeling of biosystems, machine learning,...
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On the Wiener chaos expansion of the signature of a Gaussian process
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with...
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Estimation of a Vector-Valued Function in a Stationary Gaussian Noise
In this paper, we construct a lower bound of the minimax risk in the estimation problem when we observe an unknoun pseudo-periodic vector-function in...
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Non-Gaussian Selfsimilar Stochastic Processes
This book offers an introduction to the field of stochastic analysis of Hermite processes. These selfsimilar stochastic processes with stationary...
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Simple Gaussian and Non-Gaussian SDEs
In this chapter, simple Gaussian and non-Gaussian SDEs are presented. They are appropriate paradigms to understand key dynamical and statistical...
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The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences
In this paper, we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are...
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Deep Gaussian process for multi-objective Bayesian optimization
Bayesian Optimization has become a widely used approach to perform optimization involving computationally intensive black-box functions, such as the...
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Simplified Whittle Estimators for Spectral Parameters of Stationary Linear Models with Tapered Data
AbstractThe paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of...
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On the Maximum of a Gaussian Process with Unique Maximum Point of its Variance
Gaussian random processes whose variances reach their maximum values at unique points are considered. Exact asymptotic behavior of probabilities of...