Tests of independence for pairs of paths of non-stationary Gaussian processes
Philip A. Ernst, Frederi G. Viens, Shuo Yan
TL;DR
This paper develops theoretical tests to determine independence between pairs of paths of non-stationary Gaussian processes, specifically Brownian motion and fractional Brownian motion, addressing a key challenge in stochastic process analysis.
Contribution
It introduces new theoretical methods for testing independence between paths of non-stationary Gaussian processes like Brownian motion and fBm.
Findings
Provides rigorous tests for independence between Gaussian process paths
Applicable to standard Brownian motion and fractional Brownian motion
Enhances understanding of dependence structures in non-stationary processes
Abstract
In the current work, we provide theoretical results for testing (in)dependence between pairs of paths of most commonly studied non-stationary Gaussian processes - standard Brownian motion and fractional Brownian motion (fBm). Please see the PDF version of the paper for a full abstract.
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