scholarly journals On a covariance structure of some subset of self-similar Gaussian processes

2019 ◽  
Vol 129 (6) ◽  
pp. 1903-1920
Author(s):  
V. Skorniakov
Keyword(s):  
Gaussian Processes ◽  
Covariance Structure ◽  
Self Similar

scholarly journals Symmetric Stochastic Integrals with Respect to a Class of Self-similar Gaussian Processes

2018 ◽  
Vol 32 (3) ◽  
pp. 1105-1144
Author(s):  
Daniel Harnett ◽  
Arturo Jaramillo ◽  
David Nualart
Keyword(s):  
Gaussian Processes ◽  
Stochastic Integrals ◽  
Self Similar

On the Lamperti transform of the fractional Brownian sheet

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marwa Khalil ◽  
Ciprian Tudor ◽  
Mounir Zili
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Similar Process ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Self Similar ◽  
Strictly Stationary Process

AbstractIn 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets.

scholarly journals Confirmatory Bayesian Online Change Point Detection in the Covariance Structure of Gaussian Processes

2019 ◽  
Author(s):  
Jiyeon Han ◽  
Kyowoon Lee ◽  
Anh Tong ◽  
Jaesik Choi
Keyword(s):  
Gaussian Processes ◽  
Change Point ◽  
Structural Breaks ◽  
Covariance Structure ◽  
Change Point Detection ◽  
Statistical Hypothesis ◽  
Sequential Data ◽  
Regression Error ◽  
Real World Datasets ◽  
Point Detection

In the analysis of sequential data, the detection of abrupt changes is important in predicting future events. In this paper, we propose statistical hypothesis tests for detecting covariance structure changes in locally smooth time series modeled by Gaussian Processes (GPs). We provide theoretically justified thresholds for the tests, and use them to improve Bayesian Online Change Point Detection (BOCPD) by confirming statistically significant changes and non-changes. Our Confirmatory BOCPD (CBOCPD) algorithm finds multiple structural breaks in GPs even when hyperparameters are not tuned precisely. We also provide conditions under which CBOCPD provides the lower prediction error compared to BOCPD. Experimental results on synthetic and real-world datasets show that our proposed algorithm outperforms existing methods for the prediction of nonstationarity in terms of both regression error and log-likelihood.

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