Work

Fractional Gaussian Noise: Projections, Prediction, Norms

Year: 2025

Type: article

Abstract: We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9070428

Authors: Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko

Institutions: Taras Shevchenko National University of Kyiv, University of Vaasa

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258