scholarly journals Extremes of Gaussian processes with a smooth random trend

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2267-2279 ◽  
Author(s):  
Vladimir Piterbarg ◽  
Goran Popivoda ◽  
Sinisa Stamatovic
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Exact Result ◽  
Extremes Of Gaussian Processes

Let ?(t), t ? R, be a Gaussian zero mean stationary process, and ?(t) another random process, smooth enough, being independent of ?(t). We will consider the process ?(t) + ?(t) such that conditioned on ?(t) it is a Gaussian process. We want to establish an asymptotic exact result for P (t?[o,T] sup (?(t) + ?(t)) > u), as u ? ?, where T > 0.

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (01) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

Extreme values of the cyclostationary Gaussian random process

1993 ◽  
Vol 30 (1) ◽  
pp. 82-97 ◽  
Author(s):  
D. G. Konstant ◽  
V.I. Piterbarg
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Gaussian Processes ◽  
Extreme Values ◽  
Random Processes ◽  
Mean Square ◽  
Gaussian Random Process ◽  
Covariance Functions ◽  
Limit Formula ◽  
Image Position

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

Extremes of Gaussian Processes

2004 ◽  
pp. 273-296
Author(s):  
Michael Falk ◽  
Rolf-Dieter Reiss ◽  
Jürg Hüsler
Keyword(s):  
Gaussian Processes ◽  
Extremes Of Gaussian Processes

scholarly journals Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

2019 ◽  
Vol 25 (3) ◽  
pp. 217-225
Author(s):  
Ievgen Turchyn
Keyword(s):  
Stochastic Processes ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Random Processes

Abstract We consider stochastic processes {Y(t)} which can be represented as {Y(t)=(X(t))^{s}} , {s\in\mathbb{N}} , where {X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates {Y(t)} with given accuracy and reliability in {L_{p}([0,T])} . A model for simulation with given accuracy and reliability in {L_{p}([0,T])} is also built for processes {Z(t)} which can be represented as {Z(t)=X_{1}(t)X_{2}(t)} , where {X_{1}(t)} and {X_{2}(t)} are independent stationary strictly sub-Gaussian processes.

Approximation to the exit probability of a continuous Gaussian process over a U-shaped boundary of increasing curvature

1995 ◽  
Vol 32 (2) ◽  
pp. 429-442
Author(s):  
A. N. Balabushkin
Keyword(s):  
Brownian Motion ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Simple Approximation ◽  
Minimum Point ◽  
Second Derivative ◽  
Numerical Examples ◽  
Exit Probability ◽  
Continuous Gaussian Process

A simple approximation to the probability of crossing a U-shaped boundary by a Brownian motion is given. The larger the second derivative of the curve at a minimum point, the higher the accuracy of the approximation. The result is also extended to a class of continuous Gaussian processes with definite properties. Numerical examples are given.

Predictive sets

2020 ◽  
pp. 2140006
Author(s):  
Nishant Chandgotia ◽  
Benjamin Weiss
Keyword(s):  
Harmonic Analysis ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Zero Entropy

A set [Formula: see text] is called predictive if for any zero entropy finite-valued stationary process [Formula: see text], [Formula: see text] is measurable with respect to [Formula: see text]. We know that [Formula: see text] is a predictive set. In this paper, we give sufficient conditions and necessary ones for a set to be predictive. We also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis.

Approximation to the exit probability of a continuous Gaussian process over a U-shaped boundary of increasing curvature

1995 ◽  
Vol 32 (02) ◽  
pp. 429-442
Author(s):  
A. N. Balabushkin
Keyword(s):  
Brownian Motion ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Simple Approximation ◽  
Minimum Point ◽  
Second Derivative ◽  
Numerical Examples ◽  
Exit Probability ◽  
Continuous Gaussian Process

A simple approximation to the probability of crossing a U-shaped boundary by a Brownian motion is given. The larger the second derivative of the curve at a minimum point, the higher the accuracy of the approximation. The result is also extended to a class of continuous Gaussian processes with definite properties. Numerical examples are given.

A Multi-Classification Method Based on Gaussian Processes

2012 ◽  
Vol 198-199 ◽  
pp. 1333-1337 ◽  
Author(s):  
San Xi Wei ◽  
Zong Hai Sun
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Good Accuracy ◽  
Classification Problem ◽  
Decision Time ◽  
Support Vector ◽  
Regression Problem ◽  
Multi Classification

Gaussian processes (GPs) is a very promising technology that has been applied both in the regression problem and the classification problem. In recent years, models based on Gaussian process priors have attracted much attention in the machine learning. Binary (or two-class, C=2) classification using Gaussian process is a very well-developed method. In this paper, a Multi-classification (C>2) method is illustrated, which is based on Binary GPs classification. A good accuracy can be obtained through this method. Meanwhile, a comparison about decision time and accuracy between this method and Support Vector Machine (SVM) is made during the experiments.

Sign in / Sign up

Export Citation Format

Share Document